Properties

Label 16562a
Number of curves $1$
Conductor $16562$
CM no
Rank $1$

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

Elliptic curves in class 16562a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.q1 16562a1 \([1, 0, 1, -173, 340]\) \(8281/4\) \(274299844\) \([]\) \(5760\) \(0.31277\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16562a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 16562a do not have complex multiplication.

Modular form 16562.2.a.a

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