# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("im1")

sage: E.isogeny_class()

## Elliptic curves in class 193600.im

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.im1 193600jj2 [0, -1, 0, -5812033, 5395247937] [] 4730880
193600.im2 193600jj1 [0, -1, 0, -4033, -384063] [] 430080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 193600.im do not have complex multiplication.

## Modular form 193600.2.a.im

sage: E.q_eigenform(10)

$$q + 2q^{3} + 2q^{7} + q^{9} + q^{13} + 5q^{17} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.