Properties

Label 505033.a
Number of curves $1$
Conductor $505033$
CM no
Rank $1$

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

Elliptic curves in class 505033.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
505033.a1 \([1, 0, 0, -3, 34]\) \(-3048625/505033\) \(-505033\) \([]\) \(67018\) \(-0.22628\)

Rank

sage: E.rank()
 

The elliptic curve 505033.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 505033.a do not have complex multiplication.

Modular form 505033.2.a.a

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