# Properties

 Label 570.l Number of curves $4$ Conductor $570$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 570.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.l1 570l4 $$[1, 0, 0, -52823445, -147775056075]$$ $$16300610738133468173382620881/2228489100$$ $$2228489100$$ $$$$ $$24000$$ $$2.6088$$
570.l2 570l3 $$[1, 0, 0, -3301465, -2309192023]$$ $$-3979640234041473454886161/1471455901872240$$ $$-1471455901872240$$ $$$$ $$12000$$ $$2.2623$$
570.l3 570l2 $$[1, 0, 0, -87945, -8655975]$$ $$75224183150104868881/11219310000000000$$ $$11219310000000000$$ $$$$ $$4800$$ $$1.8041$$
570.l4 570l1 $$[1, 0, 0, 9335, -737383]$$ $$89962967236397039/287450726400000$$ $$-287450726400000$$ $$$$ $$2400$$ $$1.4575$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 570.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 570.l do not have complex multiplication.

## Modular form570.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} + 2q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 