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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 19404x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.q1 | 19404x1 | \([0, 0, 0, -840, -9772]\) | \(-7168000/363\) | \(-3319481088\) | \([]\) | \(8064\) | \(0.58752\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19404x do not have complex multiplication.Modular form 19404.2.a.x
sage: E.q_eigenform(10)