sage:E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1950.c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
1950.c1 |
1950e2 |
[1,1,0,−160,−200] |
3659383421/2056392 |
257049000 |
[2] |
768 |
0.30386
|
|
1950.c2 |
1950e1 |
[1,1,0,40,0] |
54439939/32448 |
−4056000 |
[2] |
384 |
−0.042709
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 1950.c have
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+T |
3 | 1+T |
5 | 1 |
13 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
7 |
1+2T+7T2 |
1.7.c
|
11 |
1−2T+11T2 |
1.11.ac
|
17 |
1+2T+17T2 |
1.17.c
|
19 |
1+4T+19T2 |
1.19.e
|
23 |
1+23T2 |
1.23.a
|
29 |
1−4T+29T2 |
1.29.ae
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 1950.c do not have complex multiplication.
sage:E.q_eigenform(10)
sage:E.isogeny_class().matrix()
The i,j entry is the smallest degree of a cyclic isogeny between the i-th and j-th curve in the isogeny class, in the LMFDB numbering.
(1221)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.