# Properties

 Label 189618.y Number of curves $4$ Conductor $189618$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 189618.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.y1 189618m3 $$[1, 1, 1, -81785779, 284644874405]$$ $$12534210458299016895673/315581882565708$$ $$1523253471005102465772$$ $$[2]$$ $$29491200$$ $$3.1727$$
189618.y2 189618m2 $$[1, 1, 1, -5306519, 4088357021]$$ $$3423676911662954233/483711578981136$$ $$2334783402830358075024$$ $$[2, 2]$$ $$14745600$$ $$2.8262$$
189618.y3 189618m1 $$[1, 1, 1, -1399239, -573809475]$$ $$62768149033310713/6915442583808$$ $$33379520502507708672$$ $$[2]$$ $$7372800$$ $$2.4796$$ $$\Gamma_0(N)$$-optimal
189618.y4 189618m4 $$[1, 1, 1, 8656261, 21988640981]$$ $$14861225463775641287/51859390496937804$$ $$-250315372785133864787436$$ $$[2]$$ $$29491200$$ $$3.1727$$

## Rank

sage: E.rank()

The elliptic curves in class 189618.y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 189618.y do not have complex multiplication.

## Modular form 189618.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} - 2q^{10} - q^{11} - q^{12} - 4q^{14} + 2q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.