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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 257754y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.y1 | 257754y1 | \([1, 0, 1, -451277, 120346184]\) | \(-28154299464100934497/1049537371938048\) | \(-378882991269635328\) | \([]\) | \(5529600\) | \(2.1436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754y1 has rank \(2\).
Complex multiplication
The elliptic curves in class 257754y do not have complex multiplication.Modular form 257754.2.a.y
sage: E.q_eigenform(10)