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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 123627i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123627.g1 | 123627i1 | \([1, 1, 1, -1569, 24156]\) | \(-4317433/189\) | \(-18700190901\) | \([]\) | \(86400\) | \(0.73628\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123627i1 has rank \(2\).
Complex multiplication
The elliptic curves in class 123627i do not have complex multiplication.Modular form 123627.2.a.i
sage: E.q_eigenform(10)