Properties

Label 46410b
Number of curves 4
Conductor 46410
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46410.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46410b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.a3 46410b1 [1, 1, 0, -10173, 390717] [2] 73728 \(\Gamma_0(N)\)-optimal
46410.a2 46410b2 [1, 1, 0, -10493, 364413] [2, 2] 147456  
46410.a4 46410b3 [1, 1, 0, 14987, 1888117] [2] 294912  
46410.a1 46410b4 [1, 1, 0, -41093, -2836347] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 46410b have rank \(2\).

Modular form 46410.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.