E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 8112.s
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
8112.s1 |
8112bh4 |
[0,1,0,−187984,31307732] |
37159393753/1053 |
20818451976192 |
[4] |
43008 |
1.6573
|
|
8112.s2 |
8112bh3 |
[0,1,0,−52784,−4244460] |
822656953/85683 |
1694005147840512 |
[2] |
43008 |
1.6573
|
|
8112.s3 |
8112bh2 |
[0,1,0,−12224,444276] |
10218313/1521 |
30071097298944 |
[2,2] |
21504 |
1.3107
|
|
8112.s4 |
8112bh1 |
[0,1,0,1296,38676] |
12167/39 |
−771053776896 |
[2] |
10752 |
0.96411
|
Γ0(N)-optimal |
The elliptic curves in class 8112.s have
rank 1.
The elliptic curves in class 8112.s do not have complex multiplication.
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.
⎝⎜⎜⎛1424412422124421⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.