# Properties

 Label 32340.z Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.z1 32340v2 $$[0, 1, 0, -108061, -13708465]$$ $$227040091070464/4492125$$ $$2761111584000$$ $$[]$$ $$139968$$ $$1.5086$$
32340.z2 32340v1 $$[0, 1, 0, -2221, 8399]$$ $$1972117504/1082565$$ $$665405072640$$ $$$$ $$46656$$ $$0.95930$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.z have rank $$1$$.

## Complex multiplication

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

## Modular form 32340.2.a.z

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 