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Properties

Label 6069.b
Number of curves 6
Conductor 6069
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6069.b1")
sage: E.isogeny_class()

Elliptic curves in class 6069.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6069.b1 6069b5 [1, 1, 1, -226582, -41607616] 2 18432  
6069.b2 6069b3 [1, 1, 1, -14167, -654004] 4 9216  
6069.b3 6069b4 [1, 1, 1, -11277, 453444] 2 9216  
6069.b4 6069b6 [1, 1, 1, -9832, -1056292] 2 18432  
6069.b5 6069b2 [1, 1, 1, -1162, -3754] 4 4608  
6069.b6 6069b1 [1, 1, 1, 283, -286] 2 2304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 6069.b have rank \(0\).

Modular form 6069.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.