# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("570.g1")

sage: E.isogeny_class()

## Elliptic curves in class 570.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.g1 570g3 [1, 1, 1, -621, -6207]  256
570.g2 570g2 [1, 1, 1, -51, -51] [2, 2] 128
570.g3 570g1 [1, 1, 1, -31, 53]  64 $$\Gamma_0(N)$$-optimal
570.g4 570g4 [1, 1, 1, 199, -151]  256

## Rank

sage: E.rank()

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

## Modular form570.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 