# Properties

 Label 189618l Number of curves $2$ Conductor $189618$ CM no Rank $1$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 189618l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bt1 189618l1 $$[1, 0, 0, -6668321, 5675394633]$$ $$6793805286030262681/1048227429629952$$ $$5059593591384718983168$$ $$[2]$$ $$25288704$$ $$2.8881$$ $$\Gamma_0(N)$$-optimal
189618.bt2 189618l2 $$[1, 0, 0, 11610719, 31320887753]$$ $$35862531227445945959/108547797844556928$$ $$-523939487566287981082752$$ $$[2]$$ $$50577408$$ $$3.2346$$

## Rank

sage: E.rank()

The elliptic curves in class 189618l have rank $$1$$.

## Complex multiplication

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

## Modular form 189618.2.a.l

sage: E.q_eigenform(10)

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

## 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 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.