# Properties

 Label 119952.bq Number of curves $2$ Conductor $119952$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 119952.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bq1 119952k2 $$[0, 0, 0, -101871, -4537890]$$ $$574992/289$$ $$58764014966248704$$ $$$$ $$774144$$ $$1.9104$$
119952.bq2 119952k1 $$[0, 0, 0, -55566, 4991679]$$ $$1492992/17$$ $$216044172670032$$ $$$$ $$387072$$ $$1.5638$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 119952.bq have rank $$1$$.

## Complex multiplication

The elliptic curves in class 119952.bq do not have complex multiplication.

## Modular form 119952.2.a.bq

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 