# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 47190y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.w3 47190y1 $$[1, 0, 1, -729, -48644]$$ $$-24137569/561600$$ $$-994908657600$$ $$$$ $$69120$$ $$0.98289$$ $$\Gamma_0(N)$$-optimal
47190.w2 47190y2 $$[1, 0, 1, -24929, -1510324]$$ $$967068262369/4928040$$ $$8730323470440$$ $$$$ $$138240$$ $$1.3295$$
47190.w4 47190y3 $$[1, 0, 1, 6531, 1284292]$$ $$17394111071/411937500$$ $$-729772409437500$$ $$$$ $$207360$$ $$1.5322$$
47190.w1 47190y4 $$[1, 0, 1, -144719, 20099792]$$ $$189208196468929/10860320250$$ $$19239719802410250$$ $$$$ $$414720$$ $$1.8788$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.y

sage: E.q_eigenform(10)

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