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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2240.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2240.x1 | 2240z1 | \([0, 1, 0, -75, -277]\) | \(-738763264/875\) | \(-56000\) | \([]\) | \(192\) | \(-0.17735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2240.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 2240.x do not have complex multiplication.Modular form 2240.2.a.x
sage: E.q_eigenform(10)