# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 47190.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.i1 47190s4 $$[1, 1, 0, -2642036004907, -1652937758403399299]$$ $$1151287518770166280399859009187288721/877598977782384000$$ $$1554720122679137981424000$$ $$[2]$$ $$557383680$$ $$5.3340$$
47190.i2 47190s3 $$[1, 1, 0, -166298564907, -25442206797607299]$$ $$287099942490903701230558394328721/8299347173197257908489616000$$ $$14702799777496507417621772610576000$$ $$[2]$$ $$557383680$$ $$5.3340$$
47190.i3 47190s2 $$[1, 1, 0, -165127284907, -25827192712503299]$$ $$281076231077501634961715630808721/245403072288481536000000$$ $$434746512146454638397696000000$$ $$[2, 2]$$ $$278691840$$ $$4.9875$$
47190.i4 47190s1 $$[1, 1, 0, -10247284907, -409557128503299]$$ $$-67172890180943415009710808721/2029083623424000000000000$$ $$-3594645412996644864000000000000$$ $$[2]$$ $$139345920$$ $$4.6409$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.