# Properties

 Label 193200.gv Number of curves $4$ Conductor $193200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gv1")

sage: E.isogeny_class()

## Elliptic curves in class 193200.gv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.gv1 193200bk4 $$[0, 1, 0, -1205863408, -44616896812]$$ $$3029968325354577848895529/1753440696000000000000$$ $$112220204544000000000000000000$$ $$[2]$$ $$159252480$$ $$4.2637$$
193200.gv2 193200bk2 $$[0, 1, 0, -829537408, -9196291412812]$$ $$986396822567235411402169/6336721794060000$$ $$405550194819840000000000$$ $$[2]$$ $$53084160$$ $$3.7143$$
193200.gv3 193200bk1 $$[0, 1, 0, -50849408, -149494228812]$$ $$-227196402372228188089/19338934824115200$$ $$-1237691828743372800000000$$ $$[2]$$ $$26542080$$ $$3.3678$$ $$\Gamma_0(N)$$-optimal
193200.gv4 193200bk3 $$[0, 1, 0, 301464592, -5426368812]$$ $$47342661265381757089751/27397579603968000000$$ $$-1753445094653952000000000000$$ $$[2]$$ $$79626240$$ $$3.9171$$

## Rank

sage: E.rank()

The elliptic curves in class 193200.gv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 193200.gv do not have complex multiplication.

## Modular form 193200.2.a.gv

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.