Show commands:
SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 388416fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.fj3 | 388416fj1 | \([0, 1, 0, -3564, 67230]\) | \(3241792/567\) | \(875904103872\) | \([2]\) | \(655360\) | \(1.0114\) | \(\Gamma_0(N)\)-optimal |
| 388416.fj2 | 388416fj2 | \([0, 1, 0, -16569, -762489]\) | \(5088448/441\) | \(43600559837184\) | \([2, 2]\) | \(1310720\) | \(1.3580\) | |
| 388416.fj4 | 388416fj3 | \([0, 1, 0, 18111, -3502209]\) | \(830584/7203\) | \(-5697139818725376\) | \([2]\) | \(2621440\) | \(1.7045\) | |
| 388416.fj1 | 388416fj4 | \([0, 1, 0, -259329, -50916705]\) | \(2438569736/21\) | \(16609737080832\) | \([2]\) | \(2621440\) | \(1.7045\) |
Rank
sage: E.rank()
The elliptic curves in class 388416fj have rank \(0\).
Complex multiplication
The elliptic curves in class 388416fj do not have complex multiplication.Modular form 388416.2.a.fj
sage: E.q_eigenform(10)
Isogeny matrix
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
