Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4650.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.a1 | 4650d1 | \([1, 1, 0, -2019280, -1105283840]\) | \(-36422828671263791996785/239929786368\) | \(-5998244659200\) | \([]\) | \(97920\) | \(2.0543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4650.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4650.a do not have complex multiplication.Modular form 4650.2.a.a
sage: E.q_eigenform(10)