Properties

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

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

Elliptic curves in class 39039.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.i1 39039x1 \([1, 0, 0, 8193, 139554]\) \(74559407/53361\) \(-43528207003281\) \([]\) \(114816\) \(1.3054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.i1 has rank \(1\).

Complex multiplication

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

Modular form 39039.2.a.i

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