# Properties

 Label 5610r Number of curves $4$ Conductor $5610$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("r1")

E.isogeny_class()

## Elliptic curves in class 5610r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.t3 5610r1 $$[1, 0, 1, -43898, 5987756]$$ $$-9354997870579612441/10093752054144000$$ $$-10093752054144000$$ $$[6]$$ $$46080$$ $$1.7658$$ $$\Gamma_0(N)$$-optimal
5610.t2 5610r2 $$[1, 0, 1, -829978, 290863148]$$ $$63229930193881628103961/26218934428500000$$ $$26218934428500000$$ $$[6]$$ $$92160$$ $$2.1124$$
5610.t4 5610r3 $$[1, 0, 1, 367927, -108178804]$$ $$5508208700580085578359/8246033269590589440$$ $$-8246033269590589440$$ $$[2]$$ $$138240$$ $$2.3151$$
5610.t1 5610r4 $$[1, 0, 1, -2417353, -1087483252]$$ $$1562225332123379392365961/393363080510106009600$$ $$393363080510106009600$$ $$[2]$$ $$276480$$ $$2.6617$$

## Rank

sage: E.rank()

The elliptic curves in class 5610r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5610r do not have complex multiplication.

## Modular form5610.2.a.r

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.