# Properties

 Label 1610a Number of curves $2$ Conductor $1610$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1610a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1610.a2 1610a1 $$[1, -1, 0, -890, -13644]$$ $$-78013216986489/37918720000$$ $$-37918720000$$ $$$$ $$1344$$ $$0.73538$$ $$\Gamma_0(N)$$-optimal
1610.a1 1610a2 $$[1, -1, 0, -15610, -746700]$$ $$420676324562824569/56350000000$$ $$56350000000$$ $$$$ $$2688$$ $$1.0820$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1610.2.a.a

sage: E.q_eigenform(10)

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