Properties

Label 327990.r
Number of curves $6$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("327990.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
327990.r1 327990r6 [1, 0, 1, -7581633, -8035747934] [2] 12386304  
327990.r2 327990r3 [1, 0, 1, -710663, 230350238] [2] 6193152  
327990.r3 327990r4 [1, 0, 1, -475183, -124847794] [2, 2] 6193152  
327990.r4 327990r5 [1, 0, 1, -96733, -318160054] [2] 12386304  
327990.r5 327990r2 [1, 0, 1, -54683, 1806806] [2, 2] 3096576  
327990.r6 327990r1 [1, 0, 1, 12597, 218998] [2] 1548288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327990.r have rank \(0\).

Modular form 327990.2.a.r

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.