Properties

Label 83490.w
Number of curves $1$
Conductor $83490$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 83490.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83490.w1 83490bh1 \([1, 0, 1, -278, 1736]\) \(19535526241/253920\) \(30724320\) \([]\) \(42240\) \(0.24477\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83490.w1 has rank \(1\).

Complex multiplication

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

Modular form 83490.2.a.w

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