Properties

Label 1008.c
Number of curves 2
Conductor 1008
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1008.c1")
sage: E.isogeny_class()

Elliptic curves in class 1008.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.c1 1008b1 [0, 0, 0, -6, -5] 2 64 \(\Gamma_0(N)\)-optimal
1008.c2 1008b2 [0, 0, 0, 9, -26] 2 128  

Rank

sage: E.rank()

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

Modular form 1008.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.