Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 458640.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.p1 | 458640p1 | \([0, 0, 0, -1383123, -3503386222]\) | \(-832972004929/14611251200\) | \(-5132903786006917939200\) | \([]\) | \(28200960\) | \(2.8470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640.p do not have complex multiplication.Modular form 458640.2.a.p
sage: E.q_eigenform(10)