# Properties

 Label 208725p Number of curves 2 Conductor 208725 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("208725.y1")

sage: E.isogeny_class()

## Elliptic curves in class 208725p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
208725.y2 208725p1 [1, 0, 0, -69638, 102852267]  2764800 $$\Gamma_0(N)$$-optimal
208725.y1 208725p2 [1, 0, 0, -3745013, 2767499142]  5529600

## Rank

sage: E.rank()

The elliptic curves in class 208725p have rank $$1$$.

## Modular form 208725.2.a.y

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{6} - 2q^{7} + 3q^{8} + q^{9} - q^{12} + 2q^{13} + 2q^{14} - q^{16} - q^{18} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 