Properties

Label 39039.z
Number of curves $1$
Conductor $39039$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.z1 39039f1 \([0, -1, 1, -53460, 33664529]\) \(-1593413632/45196767\) \(-479289087313127091\) \([]\) \(808704\) \(2.0731\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.z1 has rank \(0\).

Complex multiplication

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

Modular form 39039.2.a.z

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - q^{7} + q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 2 q^{14} - q^{15} - 4 q^{16} - 6 q^{17} + 2 q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display