Properties

Label 16830cd
Number of curves 8
Conductor 16830
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.bk1")
sage: E.isogeny_class()

Elliptic curves in class 16830cd

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.bk8 16830cd1 [1, -1, 1, 390352, 39622547] 2 442368 \(\Gamma_0(N)\)-optimal
16830.bk7 16830cd2 [1, -1, 1, -1709168, 331875731] 4 884736  
16830.bk6 16830cd3 [1, -1, 1, -7027223, 7346695727] 6 1327104  
16830.bk5 16830cd4 [1, -1, 1, -14646488, -21340722733] 2 1769472  
16830.bk4 16830cd5 [1, -1, 1, -22364168, 40683483731] 2 1769472  
16830.bk3 16830cd6 [1, -1, 1, -113195543, 463573200431] 12 2654208  
16830.bk2 16830cd7 [1, -1, 1, -113955863, 457030494767] 6 5308416  
16830.bk1 16830cd8 [1, -1, 1, -1811128343, 29667338187311] 6 5308416  

Rank

sage: E.rank()

The elliptic curves in class 16830cd have rank \(0\).

Modular form 16830.2.a.bk

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.