Properties

Label 7920.o
Number of curves $4$
Conductor $7920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7920.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7920.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7920.o1 7920ba4 [0, 0, 0, -63903, -6217702] [2] 20736  
7920.o2 7920ba3 [0, 0, 0, -4008, -96433] [2] 10368  
7920.o3 7920ba2 [0, 0, 0, -903, -5902] [2] 6912  
7920.o4 7920ba1 [0, 0, 0, -408, 3107] [2] 3456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7920.o have rank \(1\).

Modular form 7920.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{7} - q^{11} - 4q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.