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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 12480.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.ce1 | 12480ba2 | \([0, 1, 0, -42361, -3363865]\) | \(2052450196928704/4317958125\) | \(17686356480000\) | \([2]\) | \(36864\) | \(1.4271\) | |
| 12480.ce2 | 12480ba1 | \([0, 1, 0, -1736, -89490]\) | \(-9045718037056/48125390625\) | \(-3080025000000\) | \([2]\) | \(18432\) | \(1.0805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12480.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 12480.ce do not have complex multiplication.Modular form 12480.2.a.ce
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
