# Properties

 Label 1710.n Number of curves $2$ Conductor $1710$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 1710.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.n1 1710p2 $$[1, -1, 1, -3578, -81363]$$ $$6947097508441/10687500$$ $$7791187500$$ $$$$ $$1536$$ $$0.79737$$
1710.n2 1710p1 $$[1, -1, 1, -158, -2019]$$ $$-594823321/2166000$$ $$-1579014000$$ $$$$ $$768$$ $$0.45080$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1710.n have rank $$0$$.

## Complex multiplication

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

## Modular form1710.2.a.n

sage: E.q_eigenform(10)

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

## 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. 