Properties

Label 56784bk
Number of curves 6
Conductor 56784
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("56784.bh1")
sage: E.isogeny_class()

Elliptic curves in class 56784bk

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
56784.bh6 56784bk1 [0, -1, 0, 2648, 10672] 2 73728 \(\Gamma_0(N)\)-optimal
56784.bh5 56784bk2 [0, -1, 0, -10872, 97200] 4 147456  
56784.bh3 56784bk3 [0, -1, 0, -105512, -13076688] 2 294912  
56784.bh2 56784bk4 [0, -1, 0, -132552, 18592560] 4 294912  
56784.bh4 56784bk5 [0, -1, 0, -91992, 30144048] 2 589824  
56784.bh1 56784bk6 [0, -1, 0, -2119992, 1188797232] 2 589824  

Rank

sage: E.rank()

The elliptic curves in class 56784bk have rank \(0\).

Modular form 56784.2.a.bh

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

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.