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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 83259.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83259.i1 | 83259k1 | \([0, 0, 1, -174, 1138]\) | \(-950272/363\) | \(-222551307\) | \([]\) | \(20160\) | \(0.31131\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83259.i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 83259.i do not have complex multiplication.Modular form 83259.2.a.i
sage: E.q_eigenform(10)