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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 162624.fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.fc1 | 162624ej1 | \([0, 1, 0, 7583, 608639]\) | \(50250332/194481\) | \(-186606965293056\) | \([]\) | \(491520\) | \(1.4211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162624.fc1 has rank \(2\).
Complex multiplication
The elliptic curves in class 162624.fc do not have complex multiplication.Modular form 162624.2.a.fc
sage: E.q_eigenform(10)