# Properties

 Label 47096k Number of curves $2$ Conductor $47096$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 47096k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.c2 47096k1 $$[0, 1, 0, -1789928, 1091020672]$$ $$-1041220466500/242597383$$ $$-147765842966496197632$$ $$$$ $$1290240$$ $$2.5896$$ $$\Gamma_0(N)$$-optimal
47096.c1 47096k2 $$[0, 1, 0, -30081168, 63490179616]$$ $$2471097448795250/98942809$$ $$120531948008342915072$$ $$$$ $$2580480$$ $$2.9361$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47096.2.a.k

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 