Show commands:
SageMath
E = EllipticCurve("pe1")
E.isogeny_class()
Elliptic curves in class 487872.pe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.pe1 | 487872pe1 | \([0, 0, 0, 68244, 16365008]\) | \(50250332/194481\) | \(-136036477698637824\) | \([]\) | \(3932160\) | \(1.9704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872.pe1 has rank \(0\).
Complex multiplication
The elliptic curves in class 487872.pe do not have complex multiplication.Modular form 487872.2.a.pe
sage: E.q_eigenform(10)