Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("40560.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40560ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40560.bv7 40560ca1 [0, 1, 0, -56, -26220] [2] 36864 \(\Gamma_0(N)\)-optimal
40560.bv6 40560ca2 [0, 1, 0, -13576, -604876] [2, 2] 73728  
40560.bv5 40560ca3 [0, 1, 0, -27096, 784980] [2, 2] 147456  
40560.bv4 40560ca4 [0, 1, 0, -216376, -38812396] [2] 147456  
40560.bv8 40560ca5 [0, 1, 0, 94584, 5992884] [2] 294912  
40560.bv2 40560ca6 [0, 1, 0, -365096, 84744180] [2, 2] 294912  
40560.bv3 40560ca7 [0, 1, 0, -297496, 117165140] [2] 589824  
40560.bv1 40560ca8 [0, 1, 0, -5840696, 5431120020] [2] 589824  

Rank

sage: E.rank()
 

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

Modular form 40560.2.a.bv

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.