Properties

Label 16562.z
Number of curves $1$
Conductor $16562$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 16562.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.z1 16562bx1 \([1, -1, 1, -552, 9195]\) \(-24642171/32768\) \(-24693014528\) \([]\) \(40320\) \(0.68694\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16562.z1 has rank \(2\).

Complex multiplication

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

Modular form 16562.2.a.z

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