# Properties

 Label 327990.y Number of curves $4$ Conductor $327990$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 327990.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.y1 327990y4 $$[1, 1, 1, -274211011, -1747842838417]$$ $$3833455222908263170009/14910644531250$$ $$8869199098328613281250$$ $$[2]$$ $$51609600$$ $$3.4245$$
327990.y2 327990y2 $$[1, 1, 1, -17394841, -26455414141]$$ $$978581759592931129/58281773062500$$ $$34667357806804590562500$$ $$[2, 2]$$ $$25804800$$ $$3.0779$$
327990.y3 327990y1 $$[1, 1, 1, -3249221, 1739635643]$$ $$6377838054073849/1489533786000$$ $$886009433330223306000$$ $$[2]$$ $$12902400$$ $$2.7313$$ $$\Gamma_0(N)$$-optimal
327990.y4 327990y3 $$[1, 1, 1, 13091409, -109268263641]$$ $$417152543917888871/8913566138987250$$ $$-5301997012745543621657250$$ $$[2]$$ $$51609600$$ $$3.4245$$

## Rank

sage: E.rank()

The elliptic curves in class 327990.y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 327990.y do not have complex multiplication.

## Modular form 327990.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} + q^{15} + q^{16} + 2q^{17} + q^{18} + O(q^{20})$$

## 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.