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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 45080.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45080.x1 | 45080n1 | \([0, 1, 0, -45880, -3806447]\) | \(-5674076449024/14904575\) | \(-28056133506800\) | \([]\) | \(129024\) | \(1.4557\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45080.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45080.x do not have complex multiplication.Modular form 45080.2.a.x
sage: E.q_eigenform(10)