# Properties

 Label 43120.bw Number of curves $2$ 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 43120.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43120.bw1 43120w1 $$[0, 0, 0, -1862, -29841]$$ $$379275264/15125$$ $$28471058000$$ $$[2]$$ $$34560$$ $$0.77253$$ $$\Gamma_0(N)$$-optimal
43120.bw2 43120w2 $$[0, 0, 0, 833, -109074]$$ $$2122416/171875$$ $$-5176556000000$$ $$[2]$$ $$69120$$ $$1.1191$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 43120.2.a.bw

sage: E.q_eigenform(10)

$$q + q^{5} - 3q^{9} + q^{11} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.