Properties

Label 501139.a
Number of curves $1$
Conductor $501139$
CM no
Rank $1$

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

Elliptic curves in class 501139.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
501139.a1 \([1, -1, 1, -132, -548]\) \(252555814161/501139\) \(501139\) \([]\) \(157954\) \(-0.018553\)

Rank

sage: E.rank()
 

The elliptic curve 501139.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 501139.a do not have complex multiplication.

Modular form 501139.2.a.a

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