# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.v1 32340bb2 $$[0, 1, 0, -4832355516, 128975649586020]$$ $$414354576760345737269208016/1182266314178222109375$$ $$35607667096768935154140000000$$ $$$$ $$41932800$$ $$4.3500$$
32340.v2 32340bb1 $$[0, 1, 0, -181183641, 3643311773520]$$ $$-349439858058052607328256/2844147488104248046875$$ $$-5353777725247626855468750000$$ $$$$ $$20966400$$ $$4.0034$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.v

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 