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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 40425.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40425.x1 | 40425cv1 | \([1, 0, 0, -5776513, 5343501092]\) | \(-5916387959190625/288178803\) | \(-1038308407320751875\) | \([]\) | \(1016064\) | \(2.5294\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40425.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40425.x do not have complex multiplication.Modular form 40425.2.a.x
sage: E.q_eigenform(10)