sage:E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1305.f
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
1305.f1 |
1305g1 |
[1,−1,0,−24,−37] |
2146689/145 |
105705 |
[2] |
128 |
−0.28720
|
Γ0(N)-optimal |
1305.f2 |
1305g2 |
[1,−1,0,21,−190] |
1367631/21025 |
−15327225 |
[2] |
256 |
0.059378
|
|
sage:E.rank()
The elliptic curves in class 1305.f have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
3 | 1 |
5 | 1−T |
29 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
2 |
1−T+2T2 |
1.2.ab
|
7 |
1+2T+7T2 |
1.7.c
|
11 |
1−6T+11T2 |
1.11.ag
|
13 |
1−2T+13T2 |
1.13.ac
|
17 |
1−2T+17T2 |
1.17.ac
|
19 |
1+2T+19T2 |
1.19.c
|
23 |
1+2T+23T2 |
1.23.c
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 1305.f 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.