# Properties

 Label 156090.bx Number of curves $2$ Conductor $156090$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bx1")

sage: E.isogeny_class()

## Elliptic curves in class 156090.bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156090.bx1 156090h2 $$[1, 0, 0, -28740, 1813032]$$ $$1481933914201/53916840$$ $$95516970987240$$ $$[2]$$ $$806400$$ $$1.4523$$
156090.bx2 156090h1 $$[1, 0, 0, -4540, -79408]$$ $$5841725401/1857600$$ $$3290851713600$$ $$[2]$$ $$403200$$ $$1.1057$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 156090.bx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 156090.bx do not have complex multiplication.

## Modular form 156090.2.a.bx

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} + q^{10} + q^{12} + 2q^{13} + 2q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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.