Properties

Label 1008.j
Number of curves $6$
Conductor $1008$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1008.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1008.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.j1 1008l4 [0, 0, 0, -193539, 32771842] [2] 3072  
1008.j2 1008l5 [0, 0, 0, -131619, -18202718] [2] 6144  
1008.j3 1008l3 [0, 0, 0, -14979, 249730] [2, 2] 3072  
1008.j4 1008l2 [0, 0, 0, -12099, 511810] [2, 2] 1536  
1008.j5 1008l1 [0, 0, 0, -579, 11842] [2] 768 \(\Gamma_0(N)\)-optimal
1008.j6 1008l6 [0, 0, 0, 55581, 1929058] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 1008.j have rank \(0\).

Modular form 1008.2.a.j

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{7} - 4q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.