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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 76050x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.b1 | 76050x1 | \([1, -1, 0, -1117167, 538090541]\) | \(-74168622330075/17179869184\) | \(-35717237943828480000\) | \([]\) | \(3231360\) | \(2.4713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76050x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 76050x do not have complex multiplication.Modular form 76050.2.a.x
sage: E.q_eigenform(10)