Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1638.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1638.i1 | 1638b1 | \([1, -1, 0, -33738, -2381068]\) | \(-215773279370739/447469568\) | \(-8807543506944\) | \([]\) | \(5280\) | \(1.3697\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1638.i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1638.i do not have complex multiplication.Modular form 1638.2.a.i
sage: E.q_eigenform(10)