# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.n1 32340m2 $$[0, -1, 0, -5295005, 4691413497]$$ $$227040091070464/4492125$$ $$324842016746016000$$ $$[]$$ $$979776$$ $$2.4816$$
32340.n2 32340m1 $$[0, -1, 0, -108845, -3098535]$$ $$1972117504/1082565$$ $$78284241391023360$$ $$[]$$ $$326592$$ $$1.9323$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.n

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. 