# Properties

 Label 47096a Number of curves $4$ Conductor $47096$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 47096a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.i4 47096a1 $$[0, 0, 0, 841, 48778]$$ $$432/7$$ $$-1065923391232$$ $$$$ $$48384$$ $$0.98847$$ $$\Gamma_0(N)$$-optimal
47096.i3 47096a2 $$[0, 0, 0, -15979, 731670]$$ $$740772/49$$ $$29845854954496$$ $$[2, 2]$$ $$96768$$ $$1.3350$$
47096.i2 47096a3 $$[0, 0, 0, -49619, -3365682]$$ $$11090466/2401$$ $$2924893785540608$$ $$$$ $$193536$$ $$1.6816$$
47096.i1 47096a4 $$[0, 0, 0, -251459, 48534110]$$ $$1443468546/7$$ $$8527387129856$$ $$$$ $$193536$$ $$1.6816$$

## Rank

sage: E.rank()

The elliptic curves in class 47096a have rank $$1$$.

## Complex multiplication

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

## Modular form 47096.2.a.a

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 