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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 328560.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.ba1 | 328560ba2 | \([0, -1, 0, -4498611120, 114739484990400]\) | \(511189448451769/7077888000\) | \(139405810182241584836247552000\) | \([]\) | \(531691776\) | \(4.3979\) | |
| 328560.ba2 | 328560ba1 | \([0, -1, 0, -450423360, -3600378160128]\) | \(513108539209/12597120\) | \(248112391657358680043028480\) | \([]\) | \(177230592\) | \(3.8485\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328560.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 328560.ba do not have complex multiplication.Modular form 328560.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
