Properties

Label 35322.n
Number of curves $6$
Conductor $35322$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35322.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35322.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35322.n1 35322p4 [1, 0, 1, -1130322, 462447736] [2] 401408  
35322.n2 35322p6 [1, 0, 1, -768692, -256977304] [2] 802816  
35322.n3 35322p3 [1, 0, 1, -87482, 3517400] [2, 2] 401408  
35322.n4 35322p2 [1, 0, 1, -70662, 7217800] [2, 2] 200704  
35322.n5 35322p1 [1, 0, 1, -3382, 166856] [2] 100352 \(\Gamma_0(N)\)-optimal
35322.n6 35322p5 [1, 0, 1, 324608, 27253784] [2] 802816  

Rank

sage: E.rank()
 

The elliptic curves in class 35322.n have rank \(0\).

Modular form 35322.2.a.n

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.