# Properties

 Label 161700bt Number of curves $4$ Conductor $161700$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 161700bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.dg3 161700bt1 $$[0, 1, 0, -3260133, -2300347512]$$ $$-130287139815424/2250652635$$ $$-66196757963778750000$$ $$[2]$$ $$5971968$$ $$2.6012$$ $$\Gamma_0(N)$$-optimal
161700.dg2 161700bt2 $$[0, 1, 0, -52376508, -145916628012]$$ $$33766427105425744/9823275$$ $$4622793921900000000$$ $$[2]$$ $$11943936$$ $$2.9478$$
161700.dg4 161700bt3 $$[0, 1, 0, 12615867, -11014287012]$$ $$7549996227362816/6152409907875$$ $$-180956218312896468750000$$ $$[2]$$ $$17915904$$ $$3.1505$$
161700.dg1 161700bt4 $$[0, 1, 0, -60755508, -96125082012]$$ $$52702650535889104/22020583921875$$ $$10362798711298687500000000$$ $$[2]$$ $$35831808$$ $$3.4971$$

## Rank

sage: E.rank()

The elliptic curves in class 161700bt have rank $$0$$.

## Complex multiplication

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

## Modular form 161700.2.a.bt

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - q^{11} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.