# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 47190h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.h3 47190h1 $$[1, 1, 0, -7988, 195408]$$ $$31824875809/8785920$$ $$15564793221120$$ $$$$ $$138240$$ $$1.2388$$ $$\Gamma_0(N)$$-optimal
47190.h2 47190h2 $$[1, 1, 0, -46708, -3746288]$$ $$6361447449889/294465600$$ $$521663772801600$$ $$[2, 2]$$ $$276480$$ $$1.5854$$
47190.h4 47190h3 $$[1, 1, 0, 25892, -14244248]$$ $$1083523132511/50179392120$$ $$-88895854083499320$$ $$$$ $$552960$$ $$1.9320$$
47190.h1 47190h4 $$[1, 1, 0, -738828, -244742472]$$ $$25176685646263969/57915000$$ $$102599955315000$$ $$$$ $$552960$$ $$1.9320$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47190.2.a.h

sage: E.q_eigenform(10)

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