Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 41070p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41070.l1 | 41070p1 | \([1, 0, 1, -384718, 120745856]\) | \(-2454365649169/1035763200\) | \(-2657484995710348800\) | \([]\) | \(1378944\) | \(2.2432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41070p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41070p do not have complex multiplication.Modular form 41070.2.a.p
sage: E.q_eigenform(10)