Properties

Label 46410.be
Number of curves 8
Conductor 46410
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46410.be1")
sage: E.isogeny_class()

Elliptic curves in class 46410.be

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
46410.be1 46410be8 [1, 0, 1, -7806648, 1811198446] 2 3649536  
46410.be2 46410be5 [1, 0, 1, -5949723, 5585394256] 6 1216512  
46410.be3 46410be6 [1, 0, 1, -4730848, -3936856594] 4 1824768  
46410.be4 46410be3 [1, 0, 1, -4722848, -3950910994] 2 912384  
46410.be5 46410be7 [1, 0, 1, -1783048, -8785398034] 2 3649536  
46410.be6 46410be2 [1, 0, 1, -375973, 85217756] 12 608256  
46410.be7 46410be1 [1, 0, 1, -63473, -4407244] 6 304128 \(\Gamma_0(N)\)-optimal
46410.be8 46410be4 [1, 0, 1, 197777, 322291256] 6 1216512  

Rank

sage: E.rank()

The elliptic curves in class 46410.be have rank \(1\).

Modular form 46410.2.a.be

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 4 & 6 & 12 & 12 \\ 3 & 1 & 6 & 12 & 12 & 2 & 4 & 4 \\ 2 & 6 & 1 & 2 & 2 & 3 & 6 & 6 \\ 4 & 12 & 2 & 1 & 4 & 6 & 3 & 12 \\ 4 & 12 & 2 & 4 & 1 & 6 & 12 & 3 \\ 6 & 2 & 3 & 6 & 6 & 1 & 2 & 2 \\ 12 & 4 & 6 & 3 & 12 & 2 & 1 & 4 \\ 12 & 4 & 6 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.