Properties

Label 505763.a
Number of curves $1$
Conductor $505763$
CM no
Rank $0$

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

Elliptic curves in class 505763.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
505763.a1 \([0, -1, 1, -1569, -23406]\) \(-427434241687552/505763\) \(-505763\) \([]\) \(125475\) \(0.37691\)

Rank

sage: E.rank()
 

The elliptic curve 505763.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 505763.a do not have complex multiplication.

Modular form 505763.2.a.a

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