Properties

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

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 82810bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82810.o1 82810bi1 \([1, 1, 0, -2443067, -1485239699]\) \(-1182740881/13520\) \(-18433899082513962320\) \([]\) \(2935296\) \(2.5105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82810bi1 has rank \(1\).

Complex multiplication

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

Modular form 82810.2.a.bi

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