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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 257754.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.i1 | 257754i1 | \([1, 1, 0, -346605, -78686307]\) | \(-12756247537586784625/329148288\) | \(-118822531968\) | \([]\) | \(1451520\) | \(1.6410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754.i1 has rank \(2\).
Complex multiplication
The elliptic curves in class 257754.i do not have complex multiplication.Modular form 257754.2.a.i
sage: E.q_eigenform(10)