Properties

Label 1008.g
Number of curves 4
Conductor 1008
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1008.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1008.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.g1 1008j4 [0, 0, 0, -16455, -812446] [2] 1152  
1008.g2 1008j3 [0, 0, 0, -1020, -12913] [2] 576  
1008.g3 1008j2 [0, 0, 0, -255, -502] [2] 384  
1008.g4 1008j1 [0, 0, 0, 60, -61] [2] 192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1008.g have rank \(1\).

Modular form 1008.2.a.g

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

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.