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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 20286.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20286.x1 | 20286v1 | \([1, -1, 0, -954, 99252]\) | \(-2689684081/117006336\) | \(-4179583328256\) | \([]\) | \(29952\) | \(1.1018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20286.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 20286.x do not have complex multiplication.Modular form 20286.2.a.x
sage: E.q_eigenform(10)