# Properties

 Label 190608z Number of curves 2 Conductor 190608 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("190608.cy1")

sage: E.isogeny_class()

## Elliptic curves in class 190608z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190608.cy2 190608z1 [0, 1, 0, 963, -6030]  157248 $$\Gamma_0(N)$$-optimal
190608.cy1 190608z2 [0, 1, 0, -4452, -55848]  314496

## Rank

sage: E.rank()

The elliptic curves in class 190608z have rank $$0$$.

## Modular form 190608.2.a.cy

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + 2q^{7} + q^{9} - q^{11} + 2q^{13} + 2q^{15} + 4q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 