Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 82810j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.j1 | 82810j1 | \([1, 1, 0, -688678, 242954132]\) | \(-21818208730807/2812160000\) | \(-4655799404721920000\) | \([]\) | \(1419264\) | \(2.3155\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82810j1 has rank \(2\).
Complex multiplication
The elliptic curves in class 82810j do not have complex multiplication.Modular form 82810.2.a.j
sage: E.q_eigenform(10)