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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 19404i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.x1 | 19404i1 | \([0, 0, 0, 770721, 172156502]\) | \(47061251888/39135393\) | \(-42103821240219416832\) | \([]\) | \(403200\) | \(2.4533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19404i do not have complex multiplication.Modular form 19404.2.a.i
sage: E.q_eigenform(10)