Properties

Label 116886l
Number of curves $6$
Conductor $116886$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.m6 116886l1 \([1, 0, 1, 12610133, -2212140394]\) \(125177609053596564863/73635189229502208\) \(-130449229466606161106688\) \([2]\) \(12288000\) \(3.1248\) \(\Gamma_0(N)\)-optimal
116886.m5 116886l2 \([1, 0, 1, -50900347, -17784910090]\) \(8232463578739844255617/4687062591766850064\) \(8303417292133072666229904\) \([2, 2]\) \(24576000\) \(3.4714\)  
116886.m3 116886l3 \([1, 0, 1, -521544367, 4563463980590]\) \(8856076866003496152467137/46664863048067576004\) \(82669651446297643013222244\) \([2, 2]\) \(49152000\) \(3.8180\)  
116886.m2 116886l4 \([1, 0, 1, -596424007, -5595437019394]\) \(13244420128496241770842177/29965867631164664892\) \(53086362426533704900736412\) \([2]\) \(49152000\) \(3.8180\)  
116886.m4 116886l5 \([1, 0, 1, -239264677, 9484050624794]\) \(-855073332201294509246497/21439133060285771735058\) \(-37980732003412922060731085538\) \([2]\) \(98304000\) \(4.1645\)  
116886.m1 116886l6 \([1, 0, 1, -8334128377, 292844688915986]\) \(36136672427711016379227705697/1011258101510224722\) \(1791505413569555218731042\) \([2]\) \(98304000\) \(4.1645\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886l have rank \(1\).

Complex multiplication

The elliptic curves in class 116886l do not have complex multiplication.

Modular form 116886.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} + q^{12} + 2q^{13} + q^{14} - 2q^{15} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.