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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 92778.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92778.p1 | 92778o2 | \([1, 1, 1, -3287038, -2286844645]\) | \(364376824890625/1527496992\) | \(16465218991167790368\) | \([2]\) | \(2826240\) | \(2.5420\) | |
| 92778.p2 | 92778o1 | \([1, 1, 1, -106078, -70351717]\) | \(-12246522625/191020032\) | \(-2059046057080470528\) | \([2]\) | \(1413120\) | \(2.1954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92778.p have rank \(0\).
Complex multiplication
The elliptic curves in class 92778.p do not have complex multiplication.Modular form 92778.2.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.
