# Properties

 Label 570.h Number of curves $2$ Conductor $570$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 570.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.h1 570h2 $$[1, 1, 1, -30, -75]$$ $$2992209121/54150$$ $$54150$$ $$$$ $$96$$ $$-0.29643$$
570.h2 570h1 $$[1, 1, 1, 0, -3]$$ $$-1/3420$$ $$-3420$$ $$$$ $$48$$ $$-0.64300$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form570.2.a.h

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 