# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 1710m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.p2 1710m1 $$[1, -1, 1, -62, -51]$$ $$961504803/486400$$ $$13132800$$ $$$$ $$640$$ $$0.058433$$ $$\Gamma_0(N)$$-optimal
1710.p1 1710m2 $$[1, -1, 1, -542, 4941]$$ $$651038076963/7220000$$ $$194940000$$ $$$$ $$1280$$ $$0.40501$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1710.2.a.m

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 