# Properties

 Label 47096.h Number of curves $4$ Conductor $47096$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 47096.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.h1 47096d4 $$[0, 0, 0, -3642371, -2675619634]$$ $$8773811642628/203$$ $$123647113382912$$ $$$$ $$591360$$ $$2.2268$$
47096.h2 47096d2 $$[0, 0, 0, -227911, -41705190]$$ $$8597884752/41209$$ $$6275091004182784$$ $$[2, 2]$$ $$295680$$ $$1.8802$$
47096.h3 47096d3 $$[0, 0, 0, -110171, -84727386]$$ $$-242793828/4950967$$ $$-3015629448295840768$$ $$$$ $$591360$$ $$2.2268$$
47096.h4 47096d1 $$[0, 0, 0, -21866, 121945]$$ $$121485312/69629$$ $$662671248286544$$ $$$$ $$147840$$ $$1.5336$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 47096.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 47096.h do not have complex multiplication.

## Modular form 47096.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 