# Properties

 Label 102550u Number of curves 2 Conductor 102550 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102550.u1")

sage: E.isogeny_class()

## Elliptic curves in class 102550u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.u2 102550u1 [1, -1, 1, -6480, -122353]  165888 $$\Gamma_0(N)$$-optimal
102550.u1 102550u2 [1, -1, 1, -92230, -10755353]  331776

## Rank

sage: E.rank()

The elliptic curves in class 102550u have rank $$1$$.

## Modular form 102550.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} + 2q^{13} + q^{14} + q^{16} - 4q^{17} - 3q^{18} - 6q^{19} + O(q^{20})$$

## 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. 