Properties

Label 82810bh
Number of curves $1$
Conductor $82810$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 82810bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82810.k1 82810bh1 \([1, 1, 0, -36353762, 84378900754]\) \(-27279055902727/10156250\) \(-1978225777227202343750\) \([]\) \(7827456\) \(3.0536\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82810bh1 has rank \(1\).

Complex multiplication

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

Modular form 82810.2.a.bh

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