# Properties

 Label 160446q Number of curves $2$ Conductor $160446$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 160446q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.bw1 160446q1 $$[1, 0, 0, -11316, 329088]$$ $$90458382169/25788048$$ $$45685100102928$$ $$[2]$$ $$768000$$ $$1.3277$$ $$\Gamma_0(N)$$-optimal
160446.bw2 160446q2 $$[1, 0, 0, 29824, 2180388]$$ $$1656015369191/2114999172$$ $$-3746850048147492$$ $$[2]$$ $$1536000$$ $$1.6743$$

## Rank

sage: E.rank()

The elliptic curves in class 160446q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 160446q do not have complex multiplication.

## Modular form 160446.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} + q^{8} + q^{9} + 4 q^{10} + q^{12} + q^{13} + 4 q^{15} + q^{16} - q^{17} + q^{18} - 2 q^{19} + O(q^{20})$$

## 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.