diff --git a/src/EllCrv/EllCrv.jl b/src/EllCrv/EllCrv.jl
index 264ba5cf96..52be1c875c 100644
--- a/src/EllCrv/EllCrv.jl
+++ b/src/EllCrv/EllCrv.jl
@@ -372,6 +372,12 @@ function ==(E::EllipticCurve, F::EllipticCurve)
   return a_invariants(E) == a_invariants(F) && base_field(E) == base_field(F)
 end
 
+function Base.hash(E::EllipticCurve, h::UInt)
+  h = hash(a_invariants(E), h)
+  h = hash(base_field(E), h)
+  return h
+end
+
 ################################################################################
 #
 #  Elementary invariants
diff --git a/src/EllCrv/Isomorphisms.jl b/src/EllCrv/Isomorphisms.jl
index 4cfc3be0f1..f663fb800b 100644
--- a/src/EllCrv/Isomorphisms.jl
+++ b/src/EllCrv/Isomorphisms.jl
@@ -608,6 +608,14 @@ function ==(f::EllCrvIso, g::EllCrvIso)
   return f.data == g.data && Ef == Eg && base_field(Ef) == base_field(Eg)
 end
 
+function Base.hash(f::EllCrvIso, h::UInt)
+  Ef = domain(f)
+  h = hash(f.data, h)
+  h = hash(Ef, h)
+  h = hash(base_field(Ef), h)
+  return h
+end
+
 
 ################################################################################
 #
diff --git a/src/EllCrv/LocalData.jl b/src/EllCrv/LocalData.jl
index 7f7efd63cd..75ece2ae29 100644
--- a/src/EllCrv/LocalData.jl
+++ b/src/EllCrv/LocalData.jl
@@ -817,7 +817,11 @@ end
 Return true if $K1$ and $K2$ are the same Kodaira symbol.
 """
 function ==(K1::KodairaSymbol, K2::KodairaSymbol)
-  return K1.ksymbol == K2.kymbol
+  return K1.ksymbol == K2.ksymbol
+end
+
+function Base.hash(K::KodairaSymbol, h::UInt)
+  return hash(K.ksymbol, h)
 end
 
 
diff --git a/src/FunField/Differential.jl b/src/FunField/Differential.jl
index 2e1a64ccad..b44add5dbe 100644
--- a/src/FunField/Differential.jl
+++ b/src/FunField/Differential.jl
@@ -79,6 +79,12 @@ function Base.:(==)(df::FunFldDiff, dg::FunFldDiff)
   return function_field(df) === function_field(df) && df.f == df.f
 end
 
+function Base.hash(df::FunFldDiff, h::UInt)
+  h = hash(function_field(df), h)
+  h = hash(df.f, h)
+  return h
+end
+
 ################################################################################
 #
 #  Arithmetic
diff --git a/src/FunField/Divisor.jl b/src/FunField/Divisor.jl
index ace9bbb256..e5ece7b64b 100644
--- a/src/FunField/Divisor.jl
+++ b/src/FunField/Divisor.jl
@@ -225,6 +225,8 @@ end
 Base.:(==)(D1::Divisor, D2::Divisor) = ideals(D1) == ideals(D2)
 Base.isequal(D1::Divisor, D2::Divisor) = a == b
 
+Base.hash(D::Divisor, h::UInt) = hash(ideals(D), h)
+
 ################################################################################
 #
 #  Divisor arithmetic
diff --git a/src/GrpAb/Dual.jl b/src/GrpAb/Dual.jl
index 7196e6f356..60e70e8090 100644
--- a/src/GrpAb/Dual.jl
+++ b/src/GrpAb/Dual.jl
@@ -144,6 +144,12 @@ function Base.:(==)(a::QmodnZ, b::QmodnZ)
   return a.n == b.n && a.d == b.d
 end
 
+function Base.hash(a::QmodnZ, h::UInt)
+  h = hash(a.n, h)
+  h = hash(a.d, h)
+  return h
+end
+
 function Base.:(==)(a::QmodnZElem, b::QmodnZElem)
   if parent(a).trivialmodulus
     return is_integral(a.elt - b.elt)
@@ -158,7 +164,7 @@ function Base.hash(a::QmodnZElem, h::UInt)
   if parent(a).trivialmodulus
     return hash(a.elt, h)
   end
-  error("not implemented")
+  return h
 end
 
 for T in [ZZRingElem, Integer, QQFieldElem, Rational]
diff --git a/src/NumField/ComplexEmbeddings/NfAbs.jl b/src/NumField/ComplexEmbeddings/NfAbs.jl
index 3258ffa1bb..391ad7651e 100644
--- a/src/NumField/ComplexEmbeddings/NfAbs.jl
+++ b/src/NumField/ComplexEmbeddings/NfAbs.jl
@@ -68,6 +68,12 @@ function Base.:(==)(f::AbsSimpleNumFieldEmbedding, g::AbsSimpleNumFieldEmbedding
       _absolute_index(f) == _absolute_index(g)
 end
 
+function Base.hash(f::AbsSimpleNumFieldEmbedding, h::UInt)
+  h = hash(number_field(f), h)
+  h = hash(_absolute_index(f), h)
+  return h
+end
+
 ################################################################################
 #
 #  String I/O
diff --git a/src/NumField/ComplexEmbeddings/NfRel.jl b/src/NumField/ComplexEmbeddings/NfRel.jl
index 254d57095b..e2e2c42032 100644
--- a/src/NumField/ComplexEmbeddings/NfRel.jl
+++ b/src/NumField/ComplexEmbeddings/NfRel.jl
@@ -63,6 +63,12 @@ function Base.:(==)(f::RelSimpleNumFieldEmbedding, g::RelSimpleNumFieldEmbedding
       _absolute_index(f) == _absolute_index(g)
 end
 
+function Base.hash(f::RelSimpleNumFieldEmbedding, h::UInt)
+  h = hash(number_field(f), h)
+  h = hash(_absolute_index(f), h)
+  return h
+end
+
 ################################################################################
 #
 #  Conjugate embedding
diff --git a/src/NumField/QQ.jl b/src/NumField/QQ.jl
index a6d80a2f02..7b72284e09 100644
--- a/src/NumField/QQ.jl
+++ b/src/NumField/QQ.jl
@@ -32,8 +32,6 @@ struct ZZFracIdl <: NumFieldOrderFractionalIdeal
   end
 end
 
-Base.hash(x::ZZIdl, h::UInt) = hash(gen(x), h)
-
 order(::ZZIdl) = ZZ
 
 order(::ZZFracIdl) = ZZ
@@ -93,10 +91,18 @@ function ==(I::ZZIdl, J::ZZIdl)
   return I.gen == J.gen
 end
 
+function Base.hash(I::ZZIdl, h::UInt)
+  return hash(I.gen, h)
+end
+
 function ==(I::ZZFracIdl, J::ZZFracIdl)
   return I.gen == J.gen
 end
 
+function Base.hash(I::ZZFracIdl, h::UInt)
+  return hash(I.gen, h)
+end
+
 # access
 gen(I::ZZIdl) = I.gen
 
diff --git a/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl b/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
index 222cfefdd6..24e9ecc573 100644
--- a/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
+++ b/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
@@ -91,10 +91,18 @@ function Base.:(==)(L::Line, L2::Line)
   return L.points == L2.points
 end
 
+function Base.hash(L::Line, h::UInt)
+  return hash(L.points, h)
+end
+
 function Base.:(==)(P::Polygon, P2::Polygon)
   return P.lines == P2.lines
 end
 
+function Base.hash(P::Polygon, h::UInt)
+  return hash(P.lines, h)
+end
+
 ###############################################################################
 #
 #  Lower convex hull of a set of points
diff --git a/src/NumFieldOrd/NfOrd/NfOrd.jl b/src/NumFieldOrd/NfOrd/NfOrd.jl
index 7659530ca4..7924f509e5 100644
--- a/src/NumFieldOrd/NfOrd/NfOrd.jl
+++ b/src/NumFieldOrd/NfOrd/NfOrd.jl
@@ -1139,6 +1139,14 @@ function ==(R::AbsNumFieldOrder, S::AbsNumFieldOrder)
   return hnf(R.basis_matrix) == hnf(S.basis_matrix)
 end
 
+function hash(R::AbsNumFieldOrder, h::UInt)
+  h = hash(nf(R), h)
+  h = hash(discriminant(R), h)
+  assure_has_basis_matrix(R)
+  h = hash(hnf(R.basis_matrix), h)
+  return h
+end
+
 @doc raw"""
     is_contained(R::AbsNumFieldOrder, S::AbsNumFieldOrder) -> Bool
 
@@ -1152,6 +1160,10 @@ function ==(R::AbsNumFieldOrderSet, S::AbsNumFieldOrderSet)
   return R.nf === S.nf
 end
 
+function Base.hash(R::AbsNumFieldOrderSet, h::UInt)
+  return hash(R.nf, h)
+end
+
 ################################################################################
 #
 #  Trace matrix
diff --git a/src/QuadForm/QuadBin.jl b/src/QuadForm/QuadBin.jl
index 991c3fe7b8..a75a54b032 100644
--- a/src/QuadForm/QuadBin.jl
+++ b/src/QuadForm/QuadBin.jl
@@ -295,6 +295,14 @@ function ==(f1::QuadBin, f2::QuadBin)
   return f1[1] == f2[1] && f1[2] == f2[2] && f1[3] == f2[3]
 end
 
+function Base.hash(f::QuadBin, h::UInt)
+  h = hash(base_ring(f), h)
+  h = hash(f[1], h)
+  h = hash(f[2], h)
+  h = hash(f[3], h)
+  return h
+end
+
 ###############################################################################
 #
 #   Arithmetic