Properties

Label 13167.a
Number of curves $1$
Conductor $13167$
CM no
Rank $1$

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

Elliptic curves in class 13167.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13167.a1 13167c1 \([0, 0, 1, 39, 150]\) \(242970624/501809\) \(-13548843\) \([]\) \(4992\) \(0.052851\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13167.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 13167.a do not have complex multiplication.

Modular form 13167.2.a.a

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