Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 82810.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82810.s1 82810c1 \([1, -1, 0, 1405, -28798379]\) \(219083319/256000000000\) \(-358269184000000000\) \([]\) \(1035504\) \(2.0472\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82810.s1 has rank \(0\).

Complex multiplication

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

Modular form 82810.2.a.s

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