Properties

Label 170c
Number of curves 2
Conductor 170
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("170.e1")
sage: E.isogeny_class()

Elliptic curves in class 170c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
170.e2 170c1 [1, 0, 0, 399, -919] 3 84 \(\Gamma_0(N)\)-optimal
170.e1 170c2 [1, 0, 0, -6641, -215575] 1 252  

Rank

sage: E.rank()

The elliptic curves in class 170c have rank \(0\).

Modular form 170.2.a.e

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} - 2q^{9} - q^{10} + q^{12} - q^{13} + 2q^{14} - q^{15} + q^{16} - q^{17} - 2q^{18} - q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.