# Properties

 Label 189525.bo Number of curves 4 Conductor 189525 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("189525.bo1")

sage: E.isogeny_class()

## Elliptic curves in class 189525.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189525.bo1 189525bi3 [1, 0, 1, -1015501, 393771023] [2] 2322432
189525.bo2 189525bi2 [1, 0, 1, -67876, 5244773] [2, 2] 1161216
189525.bo3 189525bi1 [1, 0, 1, -22751, -1253227] [2] 580608 $$\Gamma_0(N)$$-optimal
189525.bo4 189525bi4 [1, 0, 1, 157749, 32771023] [2] 2322432

## Rank

sage: E.rank()

The elliptic curves in class 189525.bo have rank $$1$$.

## Modular form 189525.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + q^{6} - q^{7} - 3q^{8} + q^{9} - q^{12} - 6q^{13} - q^{14} - q^{16} - 2q^{17} + q^{18} + O(q^{20})$$

## 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.