# Properties

 Label 47096.l Number of curves $2$ Conductor $47096$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 47096.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.l1 47096e2 $$[0, -1, 0, -424144, 80724444]$$ $$13854050788/3411821$$ $$2078137034626601984$$ $$[2]$$ $$806400$$ $$2.2253$$
47096.l2 47096e1 $$[0, -1, 0, 63636, 7947668]$$ $$187153328/288463$$ $$-43925637029279488$$ $$[2]$$ $$403200$$ $$1.8787$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 47096.2.a.l

sage: E.q_eigenform(10)

$$q + 2 q^{3} - 2 q^{5} + q^{7} + q^{9} + 2 q^{13} - 4 q^{15} - 6 q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.