# Properties

 Label 236992.bk Number of curves $2$ Conductor $236992$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bk1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bk1 236992bk2 $$[0, 0, 0, -29900, -1972112]$$ $$926859375/9604$$ $$30632016084992$$ $$$$ $$442368$$ $$1.4048$$
236992.bk2 236992bk1 $$[0, 0, 0, -460, -76176]$$ $$-3375/784$$ $$-2500572741632$$ $$$$ $$221184$$ $$1.0582$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 236992.bk do not have complex multiplication.

## Modular form 236992.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 4q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 