# Properties

 Label 160446.a Number of curves $4$ Conductor $160446$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 160446.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.a1 160446bn3 $$[1, 1, 0, -303668030426, 64408869849277716]$$ $$1748094148784980747354970849498497/887694600425282263291392$$ $$1572605134024013471638761702912$$ $$[2]$$ $$1134673920$$ $$5.1269$$
160446.a2 160446bn4 $$[1, 1, 0, -41539825626, -1792140629348076]$$ $$4474676144192042711273397261697/1806328356954994499451382272$$ $$3200020870375547010442590229166592$$ $$[2]$$ $$1134673920$$ $$5.1269$$
160446.a3 160446bn2 $$[1, 1, 0, -19081915866, 994944362433300]$$ $$433744050935826360922067531137/9612122270219882316693504$$ $$17028460941153004936843860639744$$ $$[2, 2]$$ $$567336960$$ $$4.7804$$
160446.a4 160446bn1 $$[1, 1, 0, 108335654, 47655976651540]$$ $$79374649975090937760383/553856914190911653543936$$ $$-981191308760965639863948804096$$ $$[2]$$ $$283668480$$ $$4.4338$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 160446.2.a.a

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.