Properties

Label 1002a
Number of curves 2
Conductor 1002
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1002.a1")
sage: E.isogeny_class()

Elliptic curves in class 1002a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.a2 1002a1 [1, 1, 0, -50, -192] 2 192 \(\Gamma_0(N)\)-optimal
1002.a1 1002a2 [1, 1, 0, -860, -10074] 2 384  

Rank

sage: E.rank()

The elliptic curves in class 1002a have rank \(0\).

Modular form 1002.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 4q^{13} + q^{16} + 6q^{17} - q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.