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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 94640cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.bd2 | 94640cy1 | \([0, -1, 0, 17520, -5870528]\) | \(30080231/768950\) | \(-15202610301132800\) | \([]\) | \(580608\) | \(1.7852\) | \(\Gamma_0(N)\)-optimal |
| 94640.bd1 | 94640cy2 | \([0, -1, 0, -158240, 161593600]\) | \(-22164361129/557375000\) | \(-11019643561472000000\) | \([]\) | \(1741824\) | \(2.3345\) |
Rank
sage: E.rank()
The elliptic curves in class 94640cy have rank \(2\).
Complex multiplication
The elliptic curves in class 94640cy do not have complex multiplication.Modular form 94640.2.a.cy
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
