Properties

Label 502237.a
Number of curves $1$
Conductor $502237$
CM no
Rank $2$

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

Elliptic curves in class 502237.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
502237.a1 \([1, 0, 0, -29, -52]\) \(2703045457/502237\) \(502237\) \([]\) \(39360\) \(-0.18794\)

Rank

sage: E.rank()
 

The elliptic curve 502237.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 502237.a do not have complex multiplication.

Modular form 502237.2.a.a

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