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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 106722.gr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.gr1 | 106722ef1 | \([1, -1, 1, -29545319, 61836728671]\) | \(-34068278205171/10307264\) | \(-862944695036146400832\) | \([]\) | \(7257600\) | \(2.9948\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722.gr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 106722.gr do not have complex multiplication.Modular form 106722.2.a.gr
sage: E.q_eigenform(10)