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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 42135.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42135.i1 | 42135i1 | \([0, 1, 1, -525265, 145678306]\) | \(5705690236075638784/30267225703125\) | \(85020637000078125\) | \([]\) | \(653184\) | \(2.0931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42135.i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 42135.i do not have complex multiplication.Modular form 42135.2.a.i
sage: E.q_eigenform(10)