Properties

Label 43120.k
Number of curves 4
Conductor 43120
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("43120.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43120.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43120.k1 43120bw4 [0, 1, 0, -347916, -79103816] [2] 248832  
43120.k2 43120bw3 [0, 1, 0, -21821, -1232330] [2] 124416  
43120.k3 43120bw2 [0, 1, 0, -4916, -76616] [2] 82944  
43120.k4 43120bw1 [0, 1, 0, -2221, 38730] [2] 41472 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43120.k have rank \(0\).

Modular form 43120.2.a.k

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} + q^{9} + q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.