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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 257754u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.u1 | 257754u1 | \([1, 0, 1, -6693670, 6748142480]\) | \(-1952934620143033/28327324536\) | \(-481098902040022073976\) | \([]\) | \(17729280\) | \(2.7731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257754u do not have complex multiplication.Modular form 257754.2.a.u
sage: E.q_eigenform(10)