sage:E = EllipticCurve("y1")
E.isogeny_class()
sage:E.rank()
The elliptic curve 5200y1 has
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
5 | 1 |
13 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
3 |
1−T+3T2 |
1.3.ab
|
7 |
1+7T2 |
1.7.a
|
11 |
1−2T+11T2 |
1.11.ac
|
17 |
1+2T+17T2 |
1.17.c
|
19 |
1+8T+19T2 |
1.19.i
|
23 |
1+T+23T2 |
1.23.b
|
29 |
1−9T+29T2 |
1.29.aj
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 5200y do not have complex multiplication.
sage:E.q_eigenform(10)
Elliptic curves in class 5200y
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
5200.j1 |
5200y1 |
[0,−1,0,4792,−1411088] |
304175/21632 |
−865280000000000 |
[] |
20160 |
1.5457
|
Γ0(N)-optimal |