sage:E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 59200.u
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
59200.u1 |
59200be1 |
[0,1,0,−85633,9616863] |
−16954786009/370 |
−1515520000000 |
[] |
165888 |
1.4532
|
Γ0(N)-optimal |
59200.u2 |
59200be2 |
[0,1,0,−29633,21992863] |
−702595369/50653000 |
−207474688000000000 |
[] |
497664 |
2.0025
|
|
59200.u3 |
59200be3 |
[0,1,0,266367,−589839137] |
510273943271/37000000000 |
−151552000000000000000 |
[] |
1492992 |
2.5518
|
|
sage:E.rank()
The elliptic curves in class 59200.u have
rank 2.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
5 | 1 |
37 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
3 |
1+2T+3T2 |
1.3.c
|
7 |
1−T+7T2 |
1.7.ab
|
11 |
1+3T+11T2 |
1.11.d
|
13 |
1+4T+13T2 |
1.13.e
|
17 |
1+3T+17T2 |
1.17.d
|
19 |
1+2T+19T2 |
1.19.c
|
23 |
1+6T+23T2 |
1.23.g
|
29 |
1+3T+29T2 |
1.29.d
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 59200.u 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.
⎝⎛139313931⎠⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.