Properties

Label 505187.a
Number of curves $1$
Conductor $505187$
CM no
Rank $1$

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

Elliptic curves in class 505187.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
505187.a1 \([0, 0, 1, -19, -47]\) \(-758550528/505187\) \(-505187\) \([]\) \(143862\) \(-0.20483\)

Rank

sage: E.rank()
 

The elliptic curve 505187.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 505187.a do not have complex multiplication.

Modular form 505187.2.a.a

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