# Properties

 Label 5610c Number of curves $2$ Conductor $5610$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.a1")

sage: E.isogeny_class()

## Elliptic curves in class 5610c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.a2 5610c1 [1, 1, 0, -22788, -7267632] [2] 49920 $$\Gamma_0(N)$$-optimal
5610.a1 5610c2 [1, 1, 0, -719108, -234128688] [2] 99840

## Rank

sage: E.rank()

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

## Modular form5610.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.