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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 37830p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37830.p1 | 37830p1 | \([1, 1, 1, 789475824, -9127268353551]\) | \(54417704466075898374229626001151/67482957163310088192000000000\) | \(-67482957163310088192000000000\) | \([]\) | \(45163008\) | \(4.2179\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 37830p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 37830p do not have complex multiplication.Modular form 37830.2.a.p
sage: E.q_eigenform(10)