Properties

Label 388080nq
Number of curves $6$
Conductor $388080$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("388080.nq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 388080nq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
388080.nq4 388080nq1 [0, 0, 0, -1869987, -984246046] [2] 6291456 \(\Gamma_0(N)\)-optimal
388080.nq3 388080nq2 [0, 0, 0, -1905267, -945176974] [2, 2] 12582912  
388080.nq2 388080nq3 [0, 0, 0, -6174147, 4786221314] [2, 2] 25165824  
388080.nq5 388080nq4 [0, 0, 0, 1799133, -4176154654] [2] 25165824  
388080.nq1 388080nq5 [0, 0, 0, -93492147, 347928497714] [2] 50331648  
388080.nq6 388080nq6 [0, 0, 0, 12841773, 28453435346] [2] 50331648  

Rank

sage: E.rank()
 

The elliptic curves in class 388080nq have rank \(0\).

Modular form 388080.2.a.nq

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.