# Properties

 Label 203280.dy Number of curves 4 Conductor 203280 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("203280.dy1")

sage: E.isogeny_class()

## Elliptic curves in class 203280.dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dy1 203280bu3 [0, 1, 0, -63870616, 196447891220] [2] 17694720
203280.dy2 203280bu2 [0, 1, 0, -4106296, 2883211604] [2, 2] 8847360
203280.dy3 203280bu1 [0, 1, 0, -969976, -319598380] [2] 4423680 $$\Gamma_0(N)$$-optimal
203280.dy4 203280bu4 [0, 1, 0, 5476904, 14348552084] [2] 17694720

## Rank

sage: E.rank()

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

## Modular form 203280.2.a.dy

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.