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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 242760.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.p1 | 242760p2 | \([0, -1, 0, -3439196, 2438066820]\) | \(728049865233616/6148477125\) | \(37992778457499936000\) | \([2]\) | \(8847360\) | \(2.5823\) | |
| 242760.p2 | 242760p1 | \([0, -1, 0, -368571, -23346180]\) | \(14337547257856/7681078125\) | \(2966440851785250000\) | \([2]\) | \(4423680\) | \(2.2357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242760.p have rank \(1\).
Complex multiplication
The elliptic curves in class 242760.p do not have complex multiplication.Modular form 242760.2.a.p
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.
