Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 123627p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123627.d1 | 123627p1 | \([0, 1, 1, -80865794, -434588502652]\) | \(-24113152/19683\) | \(-47737051551806754948094683\) | \([]\) | \(45053820\) | \(3.6254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123627p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123627p do not have complex multiplication.Modular form 123627.2.a.p
sage: E.q_eigenform(10)