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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 308763v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308763.v2 | 308763v1 | \([1, -1, 0, -597024, -180178101]\) | \(-6688239997321/121755543\) | \(-428426557298417223\) | \([2]\) | \(5677056\) | \(2.1792\) | \(\Gamma_0(N)\)-optimal |
308763.v1 | 308763v2 | \([1, -1, 0, -9593739, -11435068566]\) | \(27752351856337081/8954127\) | \(31507278516451647\) | \([2]\) | \(11354112\) | \(2.5258\) |
Rank
sage: E.rank()
The elliptic curves in class 308763v have rank \(1\).
Complex multiplication
The elliptic curves in class 308763v do not have complex multiplication.Modular form 308763.2.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.