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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 425880v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.v1 | 425880v1 | \([0, 0, 0, -316433403, -2040734495098]\) | \(26257105115938658412/1713748278480875\) | \(228702475864332115970688000\) | \([2]\) | \(154828800\) | \(3.8078\) | \(\Gamma_0(N)\)-optimal |
425880.v2 | 425880v2 | \([0, 0, 0, 262783677, -8671495783522]\) | \(7519085745831768474/126058993542015625\) | \(-33645552605404484026464000000\) | \([2]\) | \(309657600\) | \(4.1543\) |
Rank
sage: E.rank()
The elliptic curves in class 425880v have rank \(1\).
Complex multiplication
The elliptic curves in class 425880v do not have complex multiplication.Modular form 425880.2.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.