Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("170.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 170.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
170.c1 170d1 [1, 0, 1, -3, 6] [3] 12 \(\Gamma_0(N)\)-optimal
170.c2 170d2 [1, 0, 1, 22, -164] [] 36  

Rank

sage: E.rank()
 

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

Modular form 170.2.a.c

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

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 LMFDB 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 LMFDB labels.