Properties

Label 83490q
Number of curves $1$
Conductor $83490$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 83490q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83490.r1 83490q1 \([1, 1, 0, -370867, 83730541]\) \(385309196579759881/15353571409920\) \(224791639012638720\) \([]\) \(1647360\) \(2.0960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83490q1 has rank \(0\).

Complex multiplication

The elliptic curves in class 83490q do not have complex multiplication.

Modular form 83490.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 7 q^{13} - 3 q^{14} - q^{15} + q^{16} - q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display