Properties

Label 43350.cv
Number of curves 8
Conductor 43350
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("43350.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43350.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43350.cv1 43350dd7 [1, 0, 0, -38534688, -92074852008] [2] 2654208  
43350.cv2 43350dd8 [1, 0, 0, -3276688, -310994008] [2] 2654208  
43350.cv3 43350dd6 [1, 0, 0, -2409688, -1437227008] [2, 2] 1327104  
43350.cv4 43350dd5 [1, 0, 0, -2084563, 1158245867] [2] 884736  
43350.cv5 43350dd4 [1, 0, 0, -495063, -115521633] [2] 884736  
43350.cv6 43350dd2 [1, 0, 0, -133813, 17057117] [2, 2] 442368  
43350.cv7 43350dd3 [1, 0, 0, -97688, -38467008] [2] 663552  
43350.cv8 43350dd1 [1, 0, 0, 10687, 1306617] [2] 221184 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43350.cv have rank \(1\).

Modular form 43350.2.a.cv

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{12} - 2q^{13} - 4q^{14} + q^{16} + q^{18} - 4q^{19} + O(q^{20}) \)

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.