# Properties

 Label 14490.bx Number of curves $2$ Conductor $14490$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 14490.bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.bx1 14490bj1 $$[1, -1, 1, -11477, 467101]$$ $$8493409990827/185150000$$ $$3644307450000$$ $$$$ $$30720$$ $$1.1986$$ $$\Gamma_0(N)$$-optimal
14490.bx2 14490bj2 $$[1, -1, 1, 943, 1415989]$$ $$4716275733/44023437500$$ $$-866513320312500$$ $$$$ $$61440$$ $$1.5452$$

## Rank

sage: E.rank()

The elliptic curves in class 14490.bx have rank $$1$$.

## Complex multiplication

The elliptic curves in class 14490.bx do not have complex multiplication.

## Modular form 14490.2.a.bx

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 2q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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 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. 