Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.m1 39039b1 \([0, -1, 1, -5800019, -5374475299]\) \(127680722384510660804608/1761798128013\) \(297743883634197\) \([]\) \(625152\) \(2.3326\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.m1 has rank \(1\).

Complex multiplication

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

Modular form 39039.2.a.m

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