# Properties

 Label 5610.n Number of curves $4$ Conductor $5610$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.n1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.n1 5610m3 [1, 0, 1, -9989, 383402]  9216
5610.n2 5610m2 [1, 0, 1, -639, 5662] [2, 2] 4608
5610.n3 5610m1 [1, 0, 1, -139, -538]  2304 $$\Gamma_0(N)$$-optimal
5610.n4 5610m4 [1, 0, 1, 711, 26722]  9216

## Rank

sage: E.rank()

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

## Modular form5610.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 