Properties

Label 39039.w
Number of curves $1$
Conductor $39039$
CM no
Rank $1$

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

Elliptic curves in class 39039.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.w1 39039u1 \([1, 0, 1, 48, 67]\) \(74559407/53361\) \(-9018009\) \([]\) \(8832\) \(0.022972\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 39039.w do not have complex multiplication.

Modular form 39039.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + 3 q^{5} + q^{6} - q^{7} - 3 q^{8} + q^{9} + 3 q^{10} + q^{11} - q^{12} - q^{14} + 3 q^{15} - q^{16} - 3 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display