Properties

Label 116160ff
Number of curves $4$
Conductor $116160$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ff1")
 
E.isogeny_class()
 

Elliptic curves in class 116160ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.x3 116160ff1 \([0, -1, 0, -26781, -1677795]\) \(1171019776/165\) \(299322946560\) \([2]\) \(245760\) \(1.2185\) \(\Gamma_0(N)\)-optimal
116160.x2 116160ff2 \([0, -1, 0, -29201, -1353999]\) \(94875856/27225\) \(790212578918400\) \([2, 2]\) \(491520\) \(1.5651\)  
116160.x4 116160ff3 \([0, -1, 0, 77279, -9041855]\) \(439608956/556875\) \(-64653756456960000\) \([2]\) \(983040\) \(1.9116\)  
116160.x1 116160ff4 \([0, -1, 0, -174401, 27018081]\) \(5052857764/219615\) \(25497525879767040\) \([2]\) \(983040\) \(1.9116\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116160ff have rank \(1\).

Complex multiplication

The elliptic curves in class 116160ff do not have complex multiplication.

Modular form 116160.2.a.ff

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 6 q^{13} + q^{15} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.