# Properties

 Label 193600m Number of curves $2$ Conductor $193600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 193600m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bh2 193600m1 [0, 1, 0, -12833, -293537] [] 552960 $$\Gamma_0(N)$$-optimal
193600.bh1 193600m2 [0, 1, 0, -892833, -325013537] [] 1658880

## Rank

sage: E.rank()

The elliptic curves in class 193600m have rank $$0$$.

## Modular form 193600.2.a.bh

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.