# Properties

 Label 47190r Number of curves $4$ Conductor $47190$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 47190r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.r4 47190r1 $$[1, 1, 0, 7863, 351861]$$ $$30342134159/47190000$$ $$-83599963590000$$ $$[2]$$ $$245760$$ $$1.3567$$ $$\Gamma_0(N)$$-optimal
47190.r3 47190r2 $$[1, 1, 0, -52637, 3509961]$$ $$9104453457841/2226896100$$ $$3945082281812100$$ $$[2, 2]$$ $$491520$$ $$1.7033$$
47190.r2 47190r3 $$[1, 1, 0, -288587, -56846049]$$ $$1500376464746641/83599963590$$ $$148102435097463990$$ $$[2]$$ $$983040$$ $$2.0498$$
47190.r1 47190r4 $$[1, 1, 0, -784687, 267194371]$$ $$30161840495801041/2799263610$$ $$4959066240195210$$ $$[2]$$ $$983040$$ $$2.0498$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.r

sage: E.q_eigenform(10)

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

## 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 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.