Properties

Label 1008e
Number of curves 4
Conductor 1008
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1008.b1")
sage: E.isogeny_class()

Elliptic curves in class 1008e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.b4 1008e1 [0, 0, 0, -66, 1339] 2 384 \(\Gamma_0(N)\)-optimal
1008.b3 1008e2 [0, 0, 0, -2271, 41470] 4 768  
1008.b2 1008e3 [0, 0, 0, -3531, -9686] 2 1536  
1008.b1 1008e4 [0, 0, 0, -36291, 2661010] 4 1536  

Rank

sage: E.rank()

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

Modular form 1008.2.a.b

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.