Properties

Label 6160.e
Number of curves $4$
Conductor $6160$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6160.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.e1 6160j4 \([0, 0, 0, -334547, 74478994]\) \(1010962818911303721/57392720\) \(235080581120\) \([4]\) \(24576\) \(1.6485\)  
6160.e2 6160j3 \([0, 0, 0, -35027, -595054]\) \(1160306142246441/634128110000\) \(2597388738560000\) \([2]\) \(24576\) \(1.6485\)  
6160.e3 6160j2 \([0, 0, 0, -20947, 1159314]\) \(248158561089321/1859334400\) \(7615833702400\) \([2, 2]\) \(12288\) \(1.3020\)  
6160.e4 6160j1 \([0, 0, 0, -467, 41106]\) \(-2749884201/176619520\) \(-723433553920\) \([2]\) \(6144\) \(0.95539\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6160.e have rank \(0\).

Complex multiplication

The elliptic curves in class 6160.e do not have complex multiplication.

Modular form 6160.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 3q^{9} + q^{11} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.