# Properties

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

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]  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 form170.2.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. 