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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 193430a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193430.f1 | 193430a1 | \([1, -1, 1, -268437, 30436749]\) | \(3596344921161/1411372000\) | \(839516980206412000\) | \([]\) | \(6652800\) | \(2.1379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193430a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193430a do not have complex multiplication.Modular form 193430.2.a.a
sage: E.q_eigenform(10)