# Properties

 Label 203280dh Number of curves $8$ Conductor $203280$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("203280.bn1")

sage: E.isogeny_class()

## Elliptic curves in class 203280dh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.bn7 203280dh1 [0, -1, 0, -79416, -3004560] [2] 1658880 $$\Gamma_0(N)$$-optimal
203280.bn5 203280dh2 [0, -1, 0, -698936, 222996336] [2, 2] 3317760
203280.bn4 203280dh3 [0, -1, 0, -5190456, -4549785744] [2] 4976640
203280.bn2 203280dh4 [0, -1, 0, -11153336, 14340618096] [2] 6635520
203280.bn6 203280dh5 [0, -1, 0, -156856, 559519600] [2] 6635520
203280.bn3 203280dh6 [0, -1, 0, -5229176, -4478417040] [2, 2] 9953280
203280.bn1 203280dh7 [0, -1, 0, -12489176, 10692078960] [2] 19906560
203280.bn8 203280dh8 [0, -1, 0, 1411304, -15081935504] [2] 19906560

## Rank

sage: E.rank()

The elliptic curves in class 203280dh have rank $$0$$.

## Modular form 203280.2.a.bn

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.