Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 160816.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160816.j1 | 160816j1 | \([0, 1, 0, -11285, -467009]\) | \(-4194304/19\) | \(-720046564096\) | \([]\) | \(270336\) | \(1.1268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 160816.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 160816.j do not have complex multiplication.Modular form 160816.2.a.j
sage: E.q_eigenform(10)