Properties

Label 83490i
Number of curves $1$
Conductor $83490$
CM no
Rank $1$

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

Elliptic curves in class 83490i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83490.j1 83490i1 \([1, 1, 0, -30252, 56016]\) \(209140276356121/120891312000\) \(1769969698992000\) \([]\) \(483840\) \(1.6153\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83490i1 has rank \(1\).

Complex multiplication

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

Modular form 83490.2.a.i

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