Properties

Label 40362bc
Number of curves $6$
Conductor $40362$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("40362.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40362bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40362.bb5 40362bc1 [1, 0, 0, -3864, -204480] [2] 122880 \(\Gamma_0(N)\)-optimal
40362.bb4 40362bc2 [1, 0, 0, -80744, -8830416] [2, 2] 245760  
40362.bb3 40362bc3 [1, 0, 0, -99964, -4313716] [2, 2] 491520  
40362.bb1 40362bc4 [1, 0, 0, -1291604, -565099500] [2] 491520  
40362.bb6 40362bc5 [1, 0, 0, 370926, -33226362] [2] 983040  
40362.bb2 40362bc6 [1, 0, 0, -878374, 313744610] [2] 983040  

Rank

sage: E.rank()
 

The elliptic curves in class 40362bc have rank \(0\).

Modular form 40362.2.a.bb

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} - 6q^{13} - q^{14} - 2q^{15} + q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.