# Properties

 Label 47190u Number of curves $4$ Conductor $47190$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 47190u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.y4 47190u1 $$[1, 0, 1, 132371, 40035752]$$ $$144794100308831/474439680000$$ $$-840498833940480000$$ $$$$ $$737280$$ $$2.1225$$ $$\Gamma_0(N)$$-optimal
47190.y3 47190u2 $$[1, 0, 1, -1261549, 471035816]$$ $$125337052492018849/18404100000000$$ $$32603985800100000000$$ $$[2, 2]$$ $$1474560$$ $$2.4691$$
47190.y2 47190u3 $$[1, 0, 1, -5414269, -4384324408]$$ $$9908022260084596129/1047363281250000$$ $$1855467941894531250000$$ $$$$ $$2949120$$ $$2.8157$$
47190.y1 47190u4 $$[1, 0, 1, -19411549, 32915975816]$$ $$456612868287073618849/12544848030000$$ $$22223963520874830000$$ $$$$ $$2949120$$ $$2.8157$$

## Rank

sage: E.rank()

The elliptic curves in class 47190u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47190u do not have complex multiplication.

## Modular form 47190.2.a.u

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 