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Weil pairing
(
e
n
)
Codex
(
@codex,
0
)
...
Algebraic geometry
Normalization of an algebraic curve
Geometric genus
Genus one curve
Elliptic curve
Torsion point of an elliptic curve
Created
2026-09-24
Updated
2026-09-24
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The
Weil pairing
is
a
bilinear, alternating, nondegenerate
pairing
e
n
:
E
[
n
]
×
E
[
n
]
⟶
μ
n
.
(1)
For an isogeny
ϕ
and its dual, it satisfies
e
n
(
ϕP
,
Q
)
=
e
n
(
P
,
ϕ
Q
)
whenever both sides are defined.
Ancestors
(10)
Torsion point of an elliptic curve
Elliptic curve
Genus one curve
Geometric genus
Normalization of an algebraic curve
Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 125
/
3
/
c
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 125
/
4
/
d
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 125
/
5
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 125
/
5
/
c
/
Solution
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