Properties

Label 506339.a
Number of curves $1$
Conductor $506339$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 506339.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
506339.a1 \([1, 1, 1, -2589, -51784]\) \(1919244689134417/506339\) \(506339\) \([]\) \(213936\) \(0.46683\)

Rank

sage: E.rank()
 

The elliptic curve 506339.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 506339.a do not have complex multiplication.

Modular form 506339.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{15} - q^{16} + 4 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display