Properties

Label 505663.a
Number of curves $1$
Conductor $505663$
CM no
Rank $2$

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

Elliptic curves in class 505663.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
505663.a1 \([1, 1, 1, 17, 28]\) \(541343375/505663\) \(-505663\) \([]\) \(57504\) \(-0.21832\)

Rank

sage: E.rank()
 

The elliptic curve 505663.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 505663.a do not have complex multiplication.

Modular form 505663.2.a.a

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