Properties

Label 501367.a
Number of curves $1$
Conductor $501367$
CM no
Rank $1$

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

Elliptic curves in class 501367.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
501367.a1 \([1, 1, 0, -9, 32]\) \(-95443993/501367\) \(-501367\) \([]\) \(56132\) \(-0.22203\)

Rank

sage: E.rank()
 

The elliptic curve 501367.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 501367.a do not have complex multiplication.

Modular form 501367.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + q^{13} + 3 q^{14} + 4 q^{15} - q^{16} + 2 q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display