# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.w1 32340bc2 $$[0, 1, 0, -89196, -9905820]$$ $$2605772594896/108945375$$ $$3281232492384000$$ $$$$ $$165888$$ $$1.7421$$
32340.w2 32340bc1 $$[0, 1, 0, 2679, -571320]$$ $$1129201664/75796875$$ $$-142678824750000$$ $$$$ $$82944$$ $$1.3956$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.w

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - q^{11} - 4q^{13} - q^{15} - 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 