Show commands:
SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 216384fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 216384.gf4 | 216384fm1 | \([0, 1, 0, 14565087, -150674939073]\) | \(11079872671250375/324440155855872\) | \(-10006052181452386448965632\) | \([2]\) | \(44236800\) | \(3.4772\) | \(\Gamma_0(N)\)-optimal |
| 216384.gf2 | 216384fm2 | \([0, 1, 0, -351217953, -2413920920769]\) | \(155355156733986861625/8291568305839392\) | \(255720087778413413507530752\) | \([2]\) | \(88473600\) | \(3.8237\) | |
| 216384.gf3 | 216384fm3 | \([0, 1, 0, -131494113, 4139790691455]\) | \(-8152944444844179625/235342826399858688\) | \(-7258203274115016237911113728\) | \([2]\) | \(132710400\) | \(4.0265\) | |
| 216384.gf1 | 216384fm4 | \([0, 1, 0, -4755714273, 125618979138687]\) | \(385693937170561837203625/2159357734550274048\) | \(66596707529419703313537957888\) | \([2]\) | \(265420800\) | \(4.3730\) |
Rank
sage: E.rank()
The elliptic curves in class 216384fm have rank \(0\).
Complex multiplication
The elliptic curves in class 216384fm do not have complex multiplication.Modular form 216384.2.a.fm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
