# Properties

 Label 193600fw Number of curves 2 Conductor 193600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.r1")

sage: E.isogeny_class()

## Elliptic curves in class 193600fw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.r2 193600fw1 [0, 1, 0, 5647, 258223]  614400 $$\Gamma_0(N)$$-optimal
193600.r1 193600fw2 [0, 1, 0, -42753, 2726623]  1228800

## Rank

sage: E.rank()

The elliptic curves in class 193600fw have rank $$1$$.

## Modular form 193600.2.a.r

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{7} + q^{9} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 