# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.e1 32340e2 $$[0, -1, 0, -26476, 132280]$$ $$68150496976/39220335$$ $$1181243697258240$$ $$$$ $$165888$$ $$1.5817$$
32340.e2 32340e1 $$[0, -1, 0, 6599, 13210]$$ $$16880451584/9823275$$ $$-18491175687600$$ $$$$ $$82944$$ $$1.2351$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + q^{11} + q^{15} + 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 