Properties

Label 83259.i
Number of curves $1$
Conductor $83259$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 83259.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83259.i1 83259k1 \([0, 0, 1, -174, 1138]\) \(-950272/363\) \(-222551307\) \([]\) \(20160\) \(0.31131\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83259.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83259.i do not have complex multiplication.

Modular form 83259.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 2 q^{5} - 3 q^{7} + q^{11} + 2 q^{13} + 4 q^{16} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display