Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 422370.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.p1 | 422370p1 | \([1, -1, 0, 890753895, -2109229948499]\) | \(6313069436781782159/3808593750000000\) | \(-47154265704948339843750000000\) | \([]\) | \(416747520\) | \(4.1912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422370.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 422370.p do not have complex multiplication.Modular form 422370.2.a.p
sage: E.q_eigenform(10)