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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 49686j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 49686.t1 | 49686j1 | \([1, 1, 0, -223759, -40569563]\) | \(368728437337/2752512\) | \(9248916749549568\) | \([]\) | \(548352\) | \(1.8940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 49686j do not have complex multiplication.Modular form 49686.2.a.j
sage: E.q_eigenform(10)