Properties

Label 5239.d
Number of curves $1$
Conductor $5239$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 5239.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5239.d1 5239a1 \([1, -1, 0, -116, 573]\) \(-6073353/961\) \(-27447121\) \([]\) \(936\) \(0.15562\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5239.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5239.d do not have complex multiplication.

Modular form 5239.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 2 q^{14} - q^{16} + 5 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display