Properties

Label 82810bn
Number of curves $1$
Conductor $82810$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 82810bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82810.p1 82810bn1 \([1, 1, 0, 993548, 1213662416]\) \(86938307/560000\) \(-698660898171083120000\) \([]\) \(5031936\) \(2.6814\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82810bn1 has rank \(0\).

Complex multiplication

The elliptic curves in class 82810bn do not have complex multiplication.

Modular form 82810.2.a.bn

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} - 2 q^{9} - q^{10} + 5 q^{11} - q^{12} - q^{15} + q^{16} + 6 q^{17} + 2 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display