Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 388815k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388815.k1 | 388815k1 | \([0, 1, 1, -164166, -42245710]\) | \(-1376628736/1366875\) | \(-485834080420276875\) | \([]\) | \(8279040\) | \(2.0895\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 388815k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 388815k do not have complex multiplication.Modular form 388815.2.a.k
sage: E.q_eigenform(10)