E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 129948h
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
129948.l2 |
129948h1 |
[0,−1,0,−154513,−23325686] |
216727177216000/2738853 |
5155573065552 |
[2] |
414720 |
1.5855
|
Γ0(N)-optimal |
129948.l3 |
129948h2 |
[0,−1,0,−150348,−24646824] |
−12479332642000/1526829993 |
−45985285592692992 |
[2] |
829440 |
1.9321
|
|
129948.l1 |
129948h3 |
[0,−1,0,−242713,6293638] |
840033089536000/477272151837 |
898409462263539408 |
[2] |
1244160 |
2.1348
|
|
129948.l4 |
129948h4 |
[0,−1,0,960972,49144824] |
3258571509326000/1920843121977 |
−57852229749112850688 |
[2] |
2488320 |
2.4814
|
|
The elliptic curves in class 129948h have
rank 0.
The elliptic curves in class 129948h 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 Cremona numbering.
⎝⎜⎜⎛1236216336126321⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.