Properties

Label 40656bk
Number of curves 6
Conductor 40656
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("40656.l1")
sage: E.isogeny_class()

Elliptic curves in class 40656bk

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
40656.l6 40656bk1 [0, -1, 0, 1896, -7632] 2 40960 \(\Gamma_0(N)\)-optimal
40656.l5 40656bk2 [0, -1, 0, -7784, -54096] 4 81920  
40656.l3 40656bk3 [0, -1, 0, -75544, 7968688] 2 163840  
40656.l2 40656bk4 [0, -1, 0, -94904, -11205456] 4 163840  
40656.l4 40656bk5 [0, -1, 0, -65864, -18221520] 2 327680  
40656.l1 40656bk6 [0, -1, 0, -1517864, -719270352] 2 327680  

Rank

sage: E.rank()

The elliptic curves in class 40656bk have rank \(1\).

Modular form 40656.2.a.l

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.