Properties

Label 39039.l
Number of curves $1$
Conductor $39039$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.l1 39039g1 \([0, -1, 1, 1115513, -43271538]\) \(31804393380282368/18570034862379\) \(-89634011404044718611\) \([]\) \(1209600\) \(2.5179\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.l1 has rank \(2\).

Complex multiplication

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

Modular form 39039.2.a.l

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