Properties

Label 162.c
Number of curves 4
Conductor 162
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("162.c1")
sage: E.isogeny_class()

Elliptic curves in class 162.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
162.c1 162b4 [1, -1, 1, -9695, -364985] 1 126  
162.c2 162b3 [1, -1, 1, -95, -697] 3 42  
162.c3 162b1 [1, -1, 1, -5, 5] 3 6 \(\Gamma_0(N)\)-optimal
162.c4 162b2 [1, -1, 1, 25, 1] 1 18  

Rank

sage: E.rank()

The elliptic curves in class 162.c have rank \(0\).

Modular form 162.2.a.c

sage: E.q_eigenform(10)
\( q + q^{2} + q^{4} + 2q^{7} + q^{8} - 3q^{11} + 2q^{13} + 2q^{14} + q^{16} - 3q^{17} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.