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Properties

Label 46410.ct
Number of curves $4$
Conductor $46410$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 46410.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.ct1 46410cs4 \([1, 0, 0, -235935, -2888403]\) \(1452449166347993289841/836982490583229900\) \(836982490583229900\) \([2]\) \(1327104\) \(2.1286\)  
46410.ct2 46410cs2 \([1, 0, 0, -156435, 23801697]\) \(423375444074086161841/3800979000000\) \(3800979000000\) \([6]\) \(442368\) \(1.5793\)  
46410.ct3 46410cs1 \([1, 0, 0, -9555, 389025]\) \(-96475852985868721/9816049152000\) \(-9816049152000\) \([6]\) \(221184\) \(1.2327\) \(\Gamma_0(N)\)-optimal
46410.ct4 46410cs3 \([1, 0, 0, 58845, -353295]\) \(22534708906265708879/13096347846407280\) \(-13096347846407280\) \([2]\) \(663552\) \(1.7820\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46410.2.a.ct

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.