# Properties

 Label 203280ck Number of curves 8 Conductor 203280 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("203280.dg1")

sage: E.isogeny_class()

## Elliptic curves in class 203280ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dg7 203280ck1 [0, -1, 0, -963200, 364032000] [2] 3317760 $$\Gamma_0(N)$$-optimal
203280.dg6 203280ck2 [0, -1, 0, -1118080, 239260672] [2, 2] 6635520
203280.dg5 203280ck3 [0, -1, 0, -2850800, -1407059520] [2] 9953280
203280.dg8 203280ck4 [0, -1, 0, 3721920, 1753212672] [2] 13271040
203280.dg4 203280ck5 [0, -1, 0, -8436160, -9262534400] [2] 13271040
203280.dg2 203280ck6 [0, -1, 0, -42500080, -106620388928] [2, 2] 19906560
203280.dg3 203280ck7 [0, -1, 0, -39402480, -122824554048] [2] 39813120
203280.dg1 203280ck8 [0, -1, 0, -679986160, -6824703694400] [2] 39813120

## Rank

sage: E.rank()

The elliptic curves in class 203280ck have rank $$1$$.

## Modular form 203280.2.a.dg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} - 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.