Properties

Label 40560.q
Number of curves 8
Conductor 40560
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("40560.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40560.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40560.q1 40560bv7 [0, -1, 0, -14421840, 21085221312] [2] 1327104  
40560.q2 40560bv8 [0, -1, 0, -1226320, 71550400] [2] 1327104  
40560.q3 40560bv6 [0, -1, 0, -901840, 329317312] [2, 2] 663552  
40560.q4 40560bv5 [0, -1, 0, -780160, -264967808] [2] 442368  
40560.q5 40560bv4 [0, -1, 0, -185280, 26501760] [2] 442368  
40560.q6 40560bv2 [0, -1, 0, -50080, -3891200] [2, 2] 221184  
40560.q7 40560bv3 [0, -1, 0, -36560, 8817600] [2] 331776  
40560.q8 40560bv1 [0, -1, 0, 4000, -300288] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40560.q have rank \(1\).

Modular form 40560.2.a.q

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.