Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 83490j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83490.n1 83490j1 \([1, 1, 0, -12707, 555141]\) \(-128100283921/2459160\) \(-4356551948760\) \([]\) \(201600\) \(1.2193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83490j1 has rank \(1\).

Complex multiplication

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

Modular form 83490.2.a.j

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