E = EllipticCurve("ln1")
E.isogeny_class()
Elliptic curves in class 141120.ln
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
141120.ln1 |
141120jb4 |
[0,0,0,−381612,−90678224] |
546718898/405 |
4552822489743360 |
[2] |
1179648 |
1.9382
|
|
141120.ln2 |
141120jb3 |
[0,0,0,−240492,44853424] |
136835858/1875 |
21077881896960000 |
[2] |
1179648 |
1.9382
|
|
141120.ln3 |
141120jb2 |
[0,0,0,−28812,−784784] |
470596/225 |
1264672913817600 |
[2,2] |
589824 |
1.5917
|
|
141120.ln4 |
141120jb1 |
[0,0,0,6468,−93296] |
21296/15 |
−21077881896960 |
[2] |
294912 |
1.2451
|
Γ0(N)-optimal |
The elliptic curves in class 141120.ln have
rank 0.
The elliptic curves in class 141120.ln 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.