# Properties

 Label 43120bw Number of curves $4$ Conductor $43120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 43120bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43120.k4 43120bw1 [0, 1, 0, -2221, 38730] [2] 41472 $$\Gamma_0(N)$$-optimal
43120.k3 43120bw2 [0, 1, 0, -4916, -76616] [2] 82944
43120.k2 43120bw3 [0, 1, 0, -21821, -1232330] [2] 124416
43120.k1 43120bw4 [0, 1, 0, -347916, -79103816] [2] 248832

## Rank

sage: E.rank()

The elliptic curves in class 43120bw have rank $$0$$.

## Complex multiplication

The elliptic curves in class 43120bw do not have complex multiplication.

## Modular form 43120.2.a.bw

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + q^{9} + q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20})$$

## 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.