Properties

Label 20160ek
Number of curves $1$
Conductor $20160$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("ek1")
 
E.isogeny_class()
 

Elliptic curves in class 20160ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.cr1 20160ek1 \([0, 0, 0, -48, 992]\) \(-1024/35\) \(-418037760\) \([]\) \(7680\) \(0.33455\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20160ek1 has rank \(0\).

Complex multiplication

The elliptic curves in class 20160ek do not have complex multiplication.

Modular form 20160.2.a.ek

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 5 q^{11} - q^{13} - 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display