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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 351975by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
351975.by1 | 351975by1 | \([0, 1, 1, -598658, 279884219]\) | \(-32278933504/27421875\) | \(-20157597938232421875\) | \([]\) | \(13208832\) | \(2.4018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 351975by1 has rank \(1\).
Complex multiplication
The elliptic curves in class 351975by do not have complex multiplication.Modular form 351975.2.a.by
sage: E.q_eigenform(10)