Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 392784p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.p1 | 392784p1 | \([0, -1, 0, -51221, -2781603]\) | \(12845056/4509\) | \(5216996957147136\) | \([]\) | \(1632960\) | \(1.7172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 392784p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 392784p do not have complex multiplication.Modular form 392784.2.a.p
sage: E.q_eigenform(10)