Properties

Label 1008k
Number of curves 6
Conductor 1008
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1008.l1")
sage: E.isogeny_class()

Elliptic curves in class 1008k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.l6 1008k1 [0, 0, 0, 141, -142] 2 256 \(\Gamma_0(N)\)-optimal
1008.l5 1008k2 [0, 0, 0, -579, -1150] 4 512  
1008.l2 1008k3 [0, 0, 0, -7059, -227950] 4 1024  
1008.l3 1008k4 [0, 0, 0, -5619, 161138] 2 1024  
1008.l1 1008k5 [0, 0, 0, -112899, -14601022] 2 2048  
1008.l4 1008k6 [0, 0, 0, -4899, -370078] 4 2048  

Rank

sage: E.rank()

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

Modular form 1008.2.a.l

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

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.