# Properties

 Label 570m Number of curves $4$ Conductor $570$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("570.m1")

sage: E.isogeny_class()

## Elliptic curves in class 570m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.m4 570m1 [1, 0, 0, -10, 20]  96 $$\Gamma_0(N)$$-optimal
570.m3 570m2 [1, 0, 0, -190, 992] [2, 2] 192
570.m2 570m3 [1, 0, 0, -220, 650]  384
570.m1 570m4 [1, 0, 0, -3040, 64262]  384

## Rank

sage: E.rank()

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

## Modular form570.2.a.m

sage: E.q_eigenform(10)

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

## 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 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. 