↑

Properties

Label 46410.ck
Number of curves $8$
Conductor $46410$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 46410.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.ck1 46410cn8 \([1, 0, 0, -2258527940, -41313148043070]\) \(1274090022584975661628188489514561/14072533302105480763470\) \(14072533302105480763470\) \([2]\) \(25165824\) \(3.8194\)  
46410.ck2 46410cn6 \([1, 0, 0, -141270590, -644445412800]\) \(311802066473807207098058600161/1033693082103011001480900\) \(1033693082103011001480900\) \([2, 2]\) \(12582912\) \(3.4728\)  
46410.ck3 46410cn4 \([1, 0, 0, -139015370, 630861993012]\) \(297106512928238351998640242081/3977028808593750000\) \(3977028808593750000\) \([8]\) \(6291456\) \(3.1262\)  
46410.ck4 46410cn7 \([1, 0, 0, -80405240, -1203420614130]\) \(-57487943130312093140621093761/592356094985924086700006670\) \(-592356094985924086700006670\) \([2]\) \(25165824\) \(3.8194\)  
46410.ck5 46410cn3 \([1, 0, 0, -12746090, -254913900]\) \(229010110533436633465952161/132501160769452503210000\) \(132501160769452503210000\) \([2, 4]\) \(6291456\) \(3.1262\)  
46410.ck6 46410cn2 \([1, 0, 0, -8696090, 9838496100]\) \(72727020009972527154752161/265361167808100000000\) \(265361167808100000000\) \([2, 8]\) \(3145728\) \(2.7796\)  
46410.ck7 46410cn1 \([1, 0, 0, -298010, 293238372]\) \(-2926956820564562516641/35459588343029760000\) \(-35459588343029760000\) \([8]\) \(1572864\) \(2.4331\) \(\Gamma_0(N)\)-optimal
46410.ck8 46410cn5 \([1, 0, 0, 50978410, -2026455000]\) \(14651516183052242700771495839/8480668142378708755560900\) \(-8480668142378708755560900\) \([4]\) \(12582912\) \(3.4728\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46410.ck have rank \(0\).

Complex multiplication

The elliptic curves in class 46410.ck do not have complex multiplication.

Modular form 46410.2.a.ck

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 16 & 4 & 4 & 8 & 16 & 8 \\ 2 & 1 & 8 & 2 & 2 & 4 & 8 & 4 \\ 16 & 8 & 1 & 16 & 4 & 2 & 4 & 8 \\ 4 & 2 & 16 & 1 & 4 & 8 & 16 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 8 & 2 & 1 & 2 & 4 \\ 16 & 8 & 4 & 16 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.