# Properties

 Label 1610g Number of curves $2$ Conductor $1610$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1610g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1610.d2 1610g1 $$[1, 0, 0, -9120, 320512]$$ $$83890194895342081/3958384640000$$ $$3958384640000$$ $$[2]$$ $$4480$$ $$1.1780$$ $$\Gamma_0(N)$$-optimal
1610.d1 1610g2 $$[1, 0, 0, -25120, -1116288]$$ $$1753007192038126081/478174101507200$$ $$478174101507200$$ $$[2]$$ $$8960$$ $$1.5245$$

## Rank

sage: E.rank()

The elliptic curves in class 1610g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1610g do not have complex multiplication.

## Modular form1610.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - 2 q^{3} + q^{4} + q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} - 2 q^{12} - 4 q^{13} + q^{14} - 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.