Properties

Label 82810j
Number of curves $1$
Conductor $82810$
CM no
Rank $2$

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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)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} - 2 q^{9} + q^{10} + q^{11} - q^{12} + q^{15} + q^{16} - 4 q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display