sage:E = EllipticCurve("c1")
E.isogeny_class()
sage:E.rank()
The elliptic curves in class 5415c have
rank 2.
|
Bad L-factors: |
Prime |
L-Factor |
3 | 1−T |
5 | 1+T |
19 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
2 |
1+T+2T2 |
1.2.b
|
7 |
1+2T+7T2 |
1.7.c
|
11 |
1+2T+11T2 |
1.11.c
|
13 |
1−4T+13T2 |
1.13.ae
|
17 |
1−2T+17T2 |
1.17.ac
|
23 |
1+4T+23T2 |
1.23.e
|
29 |
1+4T+29T2 |
1.29.e
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 5415c 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 Cremona numbering.
(1221)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
Elliptic curves in class 5415c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
5415.h2 |
5415c1 |
[1,1,0,6852,13707] |
756058031/438615 |
−20635029094815 |
[2] |
14400 |
1.2443
|
Γ0(N)-optimal |
5415.h1 |
5415c2 |
[1,1,0,−27443,75438] |
48587168449/28048275 |
1319555807905275 |
[2] |
28800 |
1.5909
|
|