# Properties

 Label 5610q Number of curves $2$ Conductor $5610$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.r1")

sage: E.isogeny_class()

## Elliptic curves in class 5610q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.r1 5610q1 [1, 0, 1, -103, 398] [3] 1440 $$\Gamma_0(N)$$-optimal
5610.r2 5610q2 [1, 0, 1, 422, 1868] [] 4320

## Rank

sage: E.rank()

The elliptic curves in class 5610q have rank $$1$$.

## Modular form5610.2.a.r

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.