# Properties

 Label 8470.l Number of curves $2$ Conductor $8470$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8470.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.l1 8470d2 $$[1, 0, 1, -648574, 200988016]$$ $$-249353795628717731809/14000000$$ $$-1694000000$$ $$[]$$ $$72576$$ $$1.6855$$
8470.l2 8470d1 $$[1, 0, 1, -7934, 280432]$$ $$-456390127585249/17983078400$$ $$-2175952486400$$ $$[]$$ $$24192$$ $$1.1361$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8470.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8470.l do not have complex multiplication.

## Modular form8470.2.a.l

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 