# Properties

 Label 202800fw Number of curves $6$ Conductor $202800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("202800.dm1")

sage: E.isogeny_class()

## Elliptic curves in class 202800fw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
202800.dm6 202800fw1 [0, -1, 0, 1012592, -157402688] [2] 6193152 $$\Gamma_0(N)$$-optimal
202800.dm5 202800fw2 [0, -1, 0, -4395408, -1303898688] [2, 2] 12386304
202800.dm3 202800fw3 [0, -1, 0, -38195408, 89956101312] [2, 2] 24772608
202800.dm2 202800fw4 [0, -1, 0, -57123408, -166026170688] [2] 24772608
202800.dm1 202800fw5 [0, -1, 0, -609415408, 5790731701312] [2] 49545216
202800.dm4 202800fw6 [0, -1, 0, -7775408, 229279701312] [2] 49545216

## Rank

sage: E.rank()

The elliptic curves in class 202800fw have rank $$0$$.

## Modular form 202800.2.a.dm

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 4q^{11} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.