# Properties

 Label 18032.u Number of curves $2$ Conductor $18032$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 18032.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.u1 18032d2 $$[0, -1, 0, -23928, 1432544]$$ $$12576878500/1127$$ $$135772593152$$ $$$$ $$30720$$ $$1.1762$$
18032.u2 18032d1 $$[0, -1, 0, -1388, 26048]$$ $$-9826000/3703$$ $$-111527487232$$ $$$$ $$15360$$ $$0.82963$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 18032.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 18032.u do not have complex multiplication.

## Modular form 18032.2.a.u

sage: E.q_eigenform(10)

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