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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 19600x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.r1 | 19600x1 | \([0, 1, 0, -1388, -47657]\) | \(-6288640/16807\) | \(-790930697200\) | \([]\) | \(23040\) | \(0.97052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19600x do not have complex multiplication.Modular form 19600.2.a.x
sage: E.q_eigenform(10)