Properties

Label 46389k
Number of curves 6
Conductor 46389
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46389.d1")
sage: E.isogeny_class()

Elliptic curves in class 46389k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
46389.d6 46389k1 [1, 0, 0, 2163, 8712] 2 52992 \(\Gamma_0(N)\)-optimal
46389.d5 46389k2 [1, 0, 0, -8882, 68355] 4 105984  
46389.d3 46389k3 [1, 0, 0, -86197, -9688798] 2 211968  
46389.d2 46389k4 [1, 0, 0, -108287, 13686840] 4 211968  
46389.d4 46389k5 [1, 0, 0, -75152, 22229043] 2 423936  
46389.d1 46389k6 [1, 0, 0, -1731902, 877125297] 2 423936  

Rank

sage: E.rank()

The elliptic curves in class 46389k have rank \(1\).

Modular form 46389.2.a.d

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.