# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("5610.t1")

sage: E.isogeny_class()

## Elliptic curves in class 5610r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.t3 5610r1 [1, 0, 1, -43898, 5987756]  46080 $$\Gamma_0(N)$$-optimal
5610.t2 5610r2 [1, 0, 1, -829978, 290863148]  92160
5610.t4 5610r3 [1, 0, 1, 367927, -108178804]  138240
5610.t1 5610r4 [1, 0, 1, -2417353, -1087483252]  276480

## Rank

sage: E.rank()

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

## Modular form5610.2.a.t

sage: E.q_eigenform(10)

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

## 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. 