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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 77616.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.fq1 | 77616ch4 | \([0, 0, 0, -208299, -36586438]\) | \(5690357426/891\) | \(156503273084928\) | \([2]\) | \(393216\) | \(1.7347\) | |
| 77616.fq2 | 77616ch2 | \([0, 0, 0, -14259, -456190]\) | \(3650692/1089\) | \(95640889107456\) | \([2, 2]\) | \(196608\) | \(1.3881\) | |
| 77616.fq3 | 77616ch1 | \([0, 0, 0, -5439, 148862]\) | \(810448/33\) | \(724552190208\) | \([2]\) | \(98304\) | \(1.0415\) | \(\Gamma_0(N)\)-optimal |
| 77616.fq4 | 77616ch3 | \([0, 0, 0, 38661, -3049270]\) | \(36382894/43923\) | \(-7715031721334784\) | \([2]\) | \(393216\) | \(1.7347\) |
Rank
sage: E.rank()
The elliptic curves in class 77616.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.fq do not have complex multiplication.Modular form 77616.2.a.fq
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 LMFDB 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 LMFDB labels.
