Properties

Label 165649.a
Number of curves $1$
Conductor $165649$
CM no
Rank $0$

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

Elliptic curves in class 165649.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
165649.a1 165649a1 \([0, 0, 1, -165649, -16854786]\) \(110592/37\) \(168177611185614613\) \([]\) \(3255840\) \(2.0079\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 165649.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 165649.a do not have complex multiplication.

Modular form 165649.2.a.a

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