Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116160.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.dc1 116160cd4 \([0, -1, 0, -120998225, 512331200625]\) \(6749703004355978704/5671875\) \(164627620608000000\) \([2]\) \(6635520\) \(3.0391\)  
116160.dc2 116160cd3 \([0, -1, 0, -7560725, 8010763125]\) \(-26348629355659264/24169921875\) \(-43846134750000000000\) \([2]\) \(3317760\) \(2.6925\)  
116160.dc3 116160cd2 \([0, -1, 0, -1527665, 669713937]\) \(13584145739344/1195803675\) \(34708507103832883200\) \([2]\) \(2211840\) \(2.4898\)  
116160.dc4 116160cd1 \([0, -1, 0, 105835, 48657237]\) \(72268906496/606436875\) \(-1100124074712960000\) \([2]\) \(1105920\) \(2.1432\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116160.2.a.dc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2q^{7} + q^{9} + 2q^{13} - q^{15} + 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.