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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 201810.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201810.s1 | 201810cj1 | \([1, 1, 0, -13730765617, -523322438628779]\) | \(335671464244128829789081/55540601303040000000\) | \(47370081065446742027120640000000\) | \([]\) | \(843696000\) | \(4.7994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 201810.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 201810.s do not have complex multiplication.Modular form 201810.2.a.s
sage: E.q_eigenform(10)