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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 392784a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 392784.a1 | 392784a1 | \([0, -1, 0, 441768, 35791344]\) | \(19785968032823/12608077824\) | \(-6075710455463018496\) | \([]\) | \(8743680\) | \(2.2932\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 392784a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 392784a do not have complex multiplication.Modular form 392784.2.a.a
sage: E.q_eigenform(10)