# Properties

 Label 189630o Number of curves $2$ Conductor $189630$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 189630o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189630.et2 189630o1 $$[1, -1, 1, -16547, 554019]$$ $$5841725401/1857600$$ $$159319146369600$$ $$$$ $$829440$$ $$1.4290$$ $$\Gamma_0(N)$$-optimal
189630.et1 189630o2 $$[1, -1, 1, -104747, -12605421]$$ $$1481933914201/53916840$$ $$4624238223377640$$ $$$$ $$1658880$$ $$1.7756$$

## Rank

sage: E.rank()

The elliptic curves in class 189630o have rank $$1$$.

## Complex multiplication

The elliptic curves in class 189630o do not have complex multiplication.

## Modular form 189630.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 2q^{11} + 2q^{13} + q^{16} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 