# Properties

 Label 1710.h Number of curves $2$ Conductor $1710$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1710.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.h1 1710b2 $$[1, -1, 0, -399, 1805]$$ $$260549802603/104256800$$ $$2814933600$$ $$$$ $$1280$$ $$0.51130$$
1710.h2 1710b1 $$[1, -1, 0, 81, 173]$$ $$2161700757/1848320$$ $$-49904640$$ $$$$ $$640$$ $$0.16473$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1710.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1710.h do not have complex multiplication.

## Modular form1710.2.a.h

sage: E.q_eigenform(10)

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

## 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. 