Properties

Label 43120cv
Number of curves 4
Conductor 43120
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("43120.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43120cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43120.q3 43120cv1 [0, 1, 0, -43920, 68929300] [2] 663552 \(\Gamma_0(N)\)-optimal
43120.q2 43120cv2 [0, 1, 0, -2803600, 1789865748] [2] 1327104  
43120.q4 43120cv3 [0, 1, 0, 395120, -1857051372] [2] 1990656  
43120.q1 43120cv4 [0, 1, 0, -20474960, -34656469100] [2] 3981312  

Rank

sage: E.rank()
 

The elliptic curves in class 43120cv have rank \(1\).

Modular form 43120.2.a.q

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 Cremona 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 Cremona labels.