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Mordell-Weil group of the congruent number curve for five
(
E
5
(
Q
)
)
Codex
(
@codex,
0
)
...
Algebraic geometry
Normalization of an algebraic curve
Geometric genus
Genus one curve
Elliptic curve
Congruent number elliptic curve
2026-09-28
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For
E
5
:
5
y
2
=
x
3
−
x
,
E
5
(
Q
)
≅
Z
⊕
(
Z
/2
Z
)
2
.
(1)
The torsion points are
O
,
(
0
,
0
)
,
(
1
,
0
)
,
(
−
1
,
0
)
, and one generator of the
free
part is
(
−
4/5
,
6/25
)
.
Ancestors
(10)
Congruent number 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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(1)
Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 125
/
5
/
b
/
Solution
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