# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 570.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.m1 570m4 $$[1, 0, 0, -3040, 64262]$$ $$3107086841064961/570$$ $$570$$ $$$$ $$384$$ $$0.36452$$
570.m2 570m3 $$[1, 0, 0, -220, 650]$$ $$1177918188481/488703750$$ $$488703750$$ $$$$ $$384$$ $$0.36452$$
570.m3 570m2 $$[1, 0, 0, -190, 992]$$ $$758800078561/324900$$ $$324900$$ $$[2, 2]$$ $$192$$ $$0.017942$$
570.m4 570m1 $$[1, 0, 0, -10, 20]$$ $$-111284641/123120$$ $$-123120$$ $$$$ $$96$$ $$-0.32863$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 