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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 117117by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.b1 | 117117by1 | \([0, 0, 1, -302679, -64791178]\) | \(-871531204608/11022011\) | \(-38783632439923371\) | \([]\) | \(2370816\) | \(1.9929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117by1 has rank \(0\).
Complex multiplication
The elliptic curves in class 117117by do not have complex multiplication.Modular form 117117.2.a.by
sage: E.q_eigenform(10)