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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 47610v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.w2 | 47610v1 | \([1, -1, 0, -1166544, -486749952]\) | \(-1626794704081/8125440\) | \(-876882559024880640\) | \([2]\) | \(1013760\) | \(2.2904\) | \(\Gamma_0(N)\)-optimal |
47610.w1 | 47610v2 | \([1, -1, 0, -18687024, -31088020320]\) | \(6687281588245201/165600\) | \(17871247806213600\) | \([2]\) | \(2027520\) | \(2.6370\) |
Rank
sage: E.rank()
The elliptic curves in class 47610v have rank \(0\).
Complex multiplication
The elliptic curves in class 47610v do not have complex multiplication.Modular form 47610.2.a.v
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.