Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 205350.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.j1 | 205350dz1 | \([1, 1, 0, 1600, 288000]\) | \(21156119/1679616\) | \(-35928036000000\) | \([]\) | \(645120\) | \(1.2806\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 205350.j do not have complex multiplication.Modular form 205350.2.a.j
sage: E.q_eigenform(10)