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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 257600by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.by1 | 257600by1 | \([0, -1, 0, -1540833, -1772110463]\) | \(-158034076225/438790688\) | \(-1123304161280000000000\) | \([]\) | \(9216000\) | \(2.7265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257600by1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257600by do not have complex multiplication.Modular form 257600.2.a.by
sage: E.q_eigenform(10)