# Properties

 Label 236992.bh Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bh1 236992bh2 $$[0, 0, 0, -15817100, 23994686704]$$ $$926859375/9604$$ $$4534637733004090277888$$ $$$$ $$10174464$$ $$2.9725$$
236992.bh2 236992bh1 $$[0, 0, 0, -243340, 926833392]$$ $$-3375/784$$ $$-370174508816660430848$$ $$$$ $$5087232$$ $$2.6260$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.bh have rank $$0$$.

## Complex multiplication

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

## Modular form 236992.2.a.bh

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. 