# Properties

 Label 17328.u Number of curves $4$ Conductor $17328$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 17328.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17328.u1 17328bg3 $$[0, 1, 0, -586384, 172633556]$$ $$115714886617/1539$$ $$296565190078464$$ $$[4]$$ $$138240$$ $$1.9204$$
17328.u2 17328bg2 $$[0, 1, 0, -37664, 2530356]$$ $$30664297/3249$$ $$626082067943424$$ $$[2, 2]$$ $$69120$$ $$1.5738$$
17328.u3 17328bg1 $$[0, 1, 0, -8784, -276780]$$ $$389017/57$$ $$10983895928832$$ $$[2]$$ $$34560$$ $$1.2272$$ $$\Gamma_0(N)$$-optimal
17328.u4 17328bg4 $$[0, 1, 0, 48976, 12545940]$$ $$67419143/390963$$ $$-75338542175858688$$ $$[2]$$ $$138240$$ $$1.9204$$

## Rank

sage: E.rank()

The elliptic curves in class 17328.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 17328.u do not have complex multiplication.

## Modular form17328.2.a.u

sage: E.q_eigenform(10)

$$q + q^{3} - 2 q^{5} + q^{9} - 6 q^{13} - 2 q^{15} - 6 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.