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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 38808.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.ca1 | 38808cd4 | \([0, 0, 0, -208299, 36586438]\) | \(5690357426/891\) | \(156503273084928\) | \([2]\) | \(196608\) | \(1.7347\) | |
| 38808.ca2 | 38808cd2 | \([0, 0, 0, -14259, 456190]\) | \(3650692/1089\) | \(95640889107456\) | \([2, 2]\) | \(98304\) | \(1.3881\) | |
| 38808.ca3 | 38808cd1 | \([0, 0, 0, -5439, -148862]\) | \(810448/33\) | \(724552190208\) | \([2]\) | \(49152\) | \(1.0415\) | \(\Gamma_0(N)\)-optimal |
| 38808.ca4 | 38808cd3 | \([0, 0, 0, 38661, 3049270]\) | \(36382894/43923\) | \(-7715031721334784\) | \([2]\) | \(196608\) | \(1.7347\) |
Rank
sage: E.rank()
The elliptic curves in class 38808.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.ca do not have complex multiplication.Modular form 38808.2.a.ca
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.
