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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 83490.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83490.x1 | 83490z1 | \([1, 0, 1, -409588, 110509298]\) | \(-3222772836011/373770240\) | \(-881330674372515840\) | \([]\) | \(1742400\) | \(2.1796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83490.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 83490.x do not have complex multiplication.Modular form 83490.2.a.x
sage: E.q_eigenform(10)