sage:E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 338.b
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
338.b1 |
338d2 |
[1,1,0,−54421,4945517] |
−1680914269/32768 |
−347488235454464 |
[] |
1560 |
1.5836
|
|
338.b2 |
338d1 |
[1,1,0,504,−13112] |
1331/8 |
−84835994984 |
[] |
312 |
0.77890
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 338.b have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+T |
13 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
3 |
1+T+3T2 |
1.3.b
|
5 |
1−3T+5T2 |
1.5.ad
|
7 |
1−3T+7T2 |
1.7.ad
|
11 |
1+11T2 |
1.11.a
|
17 |
1+3T+17T2 |
1.17.d
|
19 |
1−6T+19T2 |
1.19.ag
|
23 |
1−6T+23T2 |
1.23.ag
|
29 |
1+29T2 |
1.29.a
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 338.b 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.
(1551)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.