# Properties

 Label 106470bu Number of curves $4$ Conductor $106470$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 106470bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.bg3 106470bu1 [1, -1, 0, -5355, 96565]  294912 $$\Gamma_0(N)$$-optimal
106470.bg2 106470bu2 [1, -1, 0, -35775, -2525639] [2, 2] 589824
106470.bg4 106470bu3 [1, -1, 0, 9855, -8557925]  1179648
106470.bg1 106470bu4 [1, -1, 0, -568125, -164679449]  1179648

## Rank

sage: E.rank()

The elliptic curves in class 106470bu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 106470bu do not have complex multiplication.

## Modular form 106470.2.a.bu

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 4q^{11} - q^{14} + q^{16} + 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 