Properties

Label 160816.j
Number of curves $1$
Conductor $160816$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 160816.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160816.j1 160816j1 \([0, 1, 0, -11285, -467009]\) \(-4194304/19\) \(-720046564096\) \([]\) \(270336\) \(1.1268\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 160816.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 160816.j do not have complex multiplication.

Modular form 160816.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} - 3 q^{7} + q^{9} + 5 q^{11} - 4 q^{13} - 2 q^{15} + 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display