# Properties

 Label 8470.h Number of curves $2$ Conductor $8470$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8470.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.h1 8470b2 $$[1, -1, 0, -820, 9246]$$ $$45844273539/350$$ $$465850$$ $$$$ $$3840$$ $$0.26223$$
8470.h2 8470b1 $$[1, -1, 0, -50, 160]$$ $$-10503459/980$$ $$-1304380$$ $$$$ $$1920$$ $$-0.084339$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8470.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8470.h do not have complex multiplication.

## Modular form8470.2.a.h

sage: E.q_eigenform(10)

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