Properties

Label 505139.a
Number of curves $1$
Conductor $505139$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 505139.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
505139.a1 \([0, 1, 1, -3266, -72941]\) \(-3853942412898304/505139\) \(-505139\) \([]\) \(248574\) \(0.50932\)

Rank

sage: E.rank()
 

The elliptic curve 505139.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 505139.a do not have complex multiplication.

Modular form 505139.2.a.a

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