Properties

Label 39326l
Number of curves 6
Conductor 39326
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("39326.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39326l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39326.m5 39326l1 [1, 1, 1, -1463, 42985] [2] 49920 \(\Gamma_0(N)\)-optimal
39326.m4 39326l2 [1, 1, 1, -29553, 1941869] [2] 99840  
39326.m6 39326l3 [1, 1, 1, 12582, -906457] [2] 149760  
39326.m3 39326l4 [1, 1, 1, -99778, -9985145] [2] 299520  
39326.m2 39326l5 [1, 1, 1, -478993, -128165393] [2] 449280  
39326.m1 39326l6 [1, 1, 1, -7670033, -8179253777] [2] 898560  

Rank

sage: E.rank()
 

The elliptic curves in class 39326l have rank \(1\).

Modular form 39326.2.a.m

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.