E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 4368.y
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
4368.y1 |
4368m4 |
[0,1,0,−13592,605412] |
271210066309732/51597 |
52835328 |
[4] |
4096 |
0.87403
|
|
4368.y2 |
4368m3 |
[0,1,0,−1632,−11100] |
469732169092/224827239 |
230223092736 |
[2] |
4096 |
0.87403
|
|
4368.y3 |
4368m2 |
[0,1,0,−852,9180] |
267492843088/3651921 |
934891776 |
[2,2] |
2048 |
0.52746
|
|
4368.y4 |
4368m1 |
[0,1,0,−7,392] |
−2725888/4198467 |
−67175472 |
[2] |
1024 |
0.18089
|
Γ0(N)-optimal |
The elliptic curves in class 4368.y have
rank 0.
The elliptic curves in class 4368.y 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.