# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("193600.be1")

sage: E.isogeny_class()

## Elliptic curves in class 193600fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.be2 193600fy1 [0, 1, 0, -40333, 1218963]  819200 $$\Gamma_0(N)$$-optimal
193600.be1 193600fy2 [0, 1, 0, -342833, -76523537]  1638400

## Rank

sage: E.rank()

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

## Modular form 193600.2.a.be

sage: E.q_eigenform(10)

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

## 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. 