Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 422331.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.r1 | 422331r1 | \([1, 1, 1, -352115, 83655788]\) | \(-50308609/2499\) | \(-239828789083727571\) | \([]\) | \(3714048\) | \(2.0961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422331.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 422331.r do not have complex multiplication.Modular form 422331.2.a.r
sage: E.q_eigenform(10)