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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 206310by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206310.x1 | 206310by1 | \([1, 0, 1, -1926894, -1035107408]\) | \(-5344780143505321/32695650000\) | \(-4840129614182850000\) | \([]\) | \(5913600\) | \(2.4243\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 206310by1 has rank \(1\).
Complex multiplication
The elliptic curves in class 206310by do not have complex multiplication.Modular form 206310.2.a.by
sage: E.q_eigenform(10)