Properties

Label 1002.d
Number of curves 2
Conductor 1002
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1002.d1")
sage: E.isogeny_class()

Elliptic curves in class 1002.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.d1 1002d2 [1, 0, 1, -125, -544] 2 288  
1002.d2 1002d1 [1, 0, 1, -5, -16] 2 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 1002.d have rank \(1\).

Modular form 1002.2.a.d

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - 2q^{10} - 4q^{11} + q^{12} + 4q^{14} + 2q^{15} + q^{16} - 4q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.