# Properties

 Label 188760.bq Number of curves $2$ Conductor $188760$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

## Elliptic curves in class 188760.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bq1 188760bb2 $$[0, -1, 0, -2587020, -1596035868]$$ $$3172116339056/10710375$$ $$6465153024254496000$$ $$$$ $$5068800$$ $$2.4735$$
188760.bq2 188760bb1 $$[0, -1, 0, -91395, -46751868]$$ $$-2237904896/23765625$$ $$-896609609502750000$$ $$$$ $$2534400$$ $$2.1269$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 188760.bq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 188760.bq do not have complex multiplication.

## Modular form 188760.2.a.bq

sage: E.q_eigenform(10)

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