Properties

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

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

Elliptic curves in class 1008.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1008.j1 1008l4 \([0, 0, 0, -193539, 32771842]\) \(268498407453697/252\) \(752467968\) \([2]\) \(3072\) \(1.4316\)  
1008.j2 1008l5 \([0, 0, 0, -131619, -18202718]\) \(84448510979617/933897762\) \(2788603774967808\) \([2]\) \(6144\) \(1.7781\)  
1008.j3 1008l3 \([0, 0, 0, -14979, 249730]\) \(124475734657/63011844\) \(188152357994496\) \([2, 2]\) \(3072\) \(1.4316\)  
1008.j4 1008l2 \([0, 0, 0, -12099, 511810]\) \(65597103937/63504\) \(189621927936\) \([2, 2]\) \(1536\) \(1.0850\)  
1008.j5 1008l1 \([0, 0, 0, -579, 11842]\) \(-7189057/16128\) \(-48157949952\) \([2]\) \(768\) \(0.73841\) \(\Gamma_0(N)\)-optimal
1008.j6 1008l6 \([0, 0, 0, 55581, 1929058]\) \(6359387729183/4218578658\) \(-12596608375529472\) \([2]\) \(6144\) \(1.7781\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1008.j do not have complex multiplication.

Modular form 1008.2.a.j

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

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.