Properties

Label 501563.a
Number of curves $1$
Conductor $501563$
CM no
Rank $2$

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

Elliptic curves in class 501563.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
501563.a1 \([0, 1, 1, 6, -32]\) \(20123648/501563\) \(-501563\) \([]\) \(65852\) \(-0.22603\)

Rank

sage: E.rank()
 

The elliptic curve 501563.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 501563.a do not have complex multiplication.

Modular form 501563.2.a.a

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