# Properties

 Label 32340.bo Number of curves $2$ Conductor $32340$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32340.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bo1 32340bo2 $$[0, 1, 0, -3740, -88572]$$ $$192143824/1815$$ $$54664431360$$ $$$$ $$36864$$ $$0.88113$$
32340.bo2 32340bo1 $$[0, 1, 0, -65, -3312]$$ $$-16384/2475$$ $$-4658900400$$ $$$$ $$18432$$ $$0.53455$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 32340.bo do not have complex multiplication.

## Modular form 32340.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{11} + 4 q^{13} + q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})$$ ## 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. 