sage:E = EllipticCurve("c1")
E.isogeny_class()
sage:E.rank()
The elliptic curve 357.c1 has
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
3 | 1+T |
7 | 1−T |
17 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
2 |
1+2T2 |
1.2.a
|
5 |
1−T+5T2 |
1.5.ab
|
11 |
1+5T+11T2 |
1.11.f
|
13 |
1+5T+13T2 |
1.13.f
|
19 |
1+5T+19T2 |
1.19.f
|
23 |
1+T+23T2 |
1.23.b
|
29 |
1+6T+29T2 |
1.29.g
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 357.c do not have complex multiplication.
sage:E.q_eigenform(10)
Elliptic curves in class 357.c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
357.c1 |
357b1 |
[0,−1,1,−5,−16] |
−16777216/122451 |
−122451 |
[] |
32 |
−0.34061
|
Γ0(N)-optimal |