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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 585i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
585.c1 | 585i1 | \([0, 0, 1, -597, 8820]\) | \(-32278933504/27421875\) | \(-19990546875\) | \([]\) | \(672\) | \(0.67416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 585i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 585i do not have complex multiplication.Modular form 585.2.a.i
sage: E.q_eigenform(10)