Properties

Label 182.d
Number of curves 3
Conductor 182
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("182.d1")
sage: E.isogeny_class()

Elliptic curves in class 182.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
182.d1 182b3 [1, 0, 0, -15663, -755809] 1 108  
182.d2 182b2 [1, 0, 0, -193, -1055] 3 36  
182.d3 182b1 [1, 0, 0, 7, -7] 3 12 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 182.d have rank \(0\).

Modular form 182.2.a.d

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} - 3q^{11} + q^{12} + q^{13} + q^{14} + q^{16} - 2q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.