Properties

Label 7440.j
Number of curves $6$
Conductor $7440$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7440.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7440.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7440.j1 7440o5 [0, -1, 0, -4920320, 4202499840] [4] 98304  
7440.j2 7440o4 [0, -1, 0, -307520, 65740800] [2, 4] 49152  
7440.j3 7440o6 [0, -1, 0, -302720, 67887360] [4] 98304  
7440.j4 7440o3 [0, -1, 0, -59200, -4302848] [2] 49152  
7440.j5 7440o2 [0, -1, 0, -19520, 998400] [2, 2] 24576  
7440.j6 7440o1 [0, -1, 0, 960, 64512] [2] 12288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7440.j have rank \(0\).

Modular form 7440.2.a.j

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.