# Properties

 Label 243600cv Number of curves $6$ Conductor $243600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("243600.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 243600cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
243600.cv5 243600cv1 [0, -1, 0, -313608, -72270288] [2] 3145728 $$\Gamma_0(N)$$-optimal
243600.cv4 243600cv2 [0, -1, 0, -5115608, -4451694288] [2, 2] 6291456
243600.cv3 243600cv3 [0, -1, 0, -5213608, -4272158288] [2, 2] 12582912
243600.cv1 243600cv4 [0, -1, 0, -81849608, -284991198288] [2] 12582912
243600.cv2 243600cv5 [0, -1, 0, -16987608, 21913217712] [2] 25165824
243600.cv6 243600cv6 [0, -1, 0, 4992392, -18968798288] [2] 25165824

## Rank

sage: E.rank()

The elliptic curves in class 243600cv have rank $$0$$.

## Modular form 243600.2.a.cv

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.