# Properties

 Label 193600ge Number of curves 4 Conductor 193600 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.u1")

sage: E.isogeny_class()

## Elliptic curves in class 193600ge

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.u4 193600ge1 [0, 1, 0, -548533, -153346437] [2] 3317760 $$\Gamma_0(N)$$-optimal
193600.u3 193600ge2 [0, 1, 0, -1214033, 290542063] [2] 6635520
193600.u2 193600ge3 [0, 1, 0, -5388533, 4751993563] [2] 9953280
193600.u1 193600ge4 [0, 1, 0, -85914033, 306481042063] [2] 19906560

## Rank

sage: E.rank()

The elliptic curves in class 193600ge have rank $$2$$.

## Modular form 193600.2.a.u

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.