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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 92778n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92778.l2 | 92778n1 | \([1, 1, 1, -7791189, -8381634693]\) | \(-4852301599161073/5264989632\) | \(-56752456948280468928\) | \([2]\) | \(5087232\) | \(2.7061\) | \(\Gamma_0(N)\)-optimal |
| 92778.l1 | 92778n2 | \([1, 1, 1, -124691469, -535975978389]\) | \(19890549858062266993/23380056\) | \(252018658028078424\) | \([2]\) | \(10174464\) | \(3.0527\) |
Rank
sage: E.rank()
The elliptic curves in class 92778n have rank \(1\).
Complex multiplication
The elliptic curves in class 92778n do not have complex multiplication.Modular form 92778.2.a.n
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 Cremona 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 Cremona labels.
