# Properties

 Label 193600fa Number of curves 4 Conductor 193600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.ix1")

sage: E.isogeny_class()

## Elliptic curves in class 193600fa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.ix4 193600fa1 [0, -1, 0, -548533, 153346437]  3317760 $$\Gamma_0(N)$$-optimal
193600.ix3 193600fa2 [0, -1, 0, -1214033, -290542063]  6635520
193600.ix2 193600fa3 [0, -1, 0, -5388533, -4751993563]  9953280
193600.ix1 193600fa4 [0, -1, 0, -85914033, -306481042063]  19906560

## Rank

sage: E.rank()

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

## Modular form 193600.2.a.ix

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 