Properties

Label 94710.cx
Number of curves $4$
Conductor $94710$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 94710.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94710.cx1 94710cy4 \([1, 0, 0, -3707515865, -86890877578125]\) \(5636023126211175233366348044223761/22086834363269135887350\) \(22086834363269135887350\) \([2]\) \(67200000\) \(3.9231\)  
94710.cx2 94710cy3 \([1, 0, 0, -231829835, -1356329791443]\) \(1377944388663050233311549787441/2723783207744786460148260\) \(2723783207744786460148260\) \([2]\) \(33600000\) \(3.5766\)  
94710.cx3 94710cy2 \([1, 0, 0, -13736615, 11732181225]\) \(286657225480543563498731761/106415753000070937500000\) \(106415753000070937500000\) \([10]\) \(13440000\) \(3.1184\)  
94710.cx4 94710cy1 \([1, 0, 0, -12142535, 16280729097]\) \(197993898174778925173824241/58723661173161600000\) \(58723661173161600000\) \([10]\) \(6720000\) \(2.7719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94710.cx have rank \(1\).

Complex multiplication

The elliptic curves in class 94710.cx do not have complex multiplication.

Modular form 94710.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 6 q^{13} + q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.