# Properties

 Label 161700.et Number of curves $4$ Conductor $161700$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("et1")

sage: E.isogeny_class()

## Elliptic curves in class 161700.et

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.et1 161700bi4 $$[0, 1, 0, -306245508, 2062676933988]$$ $$6749703004355978704/5671875$$ $$2669161687500000000$$ $$[2]$$ $$14929920$$ $$3.2712$$
161700.et2 161700bi3 $$[0, 1, 0, -19136133, 32239433988]$$ $$-26348629355659264/24169921875$$ $$-710891784667968750000$$ $$[2]$$ $$7464960$$ $$2.9247$$
161700.et3 161700bi2 $$[0, 1, 0, -3866508, 2693315988]$$ $$13584145739344/1195803675$$ $$562740426240300000000$$ $$[2]$$ $$4976640$$ $$2.7219$$
161700.et4 161700bi1 $$[0, 1, 0, 267867, 196153488]$$ $$72268906496/606436875$$ $$-17836672976718750000$$ $$[2]$$ $$2488320$$ $$2.3753$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 161700.et have rank $$1$$.

## Complex multiplication

The elliptic curves in class 161700.et do not have complex multiplication.

## Modular form 161700.2.a.et

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + q^{11} + 2q^{13} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.