# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("u1")

E.isogeny_class()

## Elliptic curves in class 5610.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.u1 5610v2 $$[1, 0, 1, -688, 6806]$$ $$35940267099001/448014600$$ $$448014600$$ $$[2]$$ $$4608$$ $$0.46972$$
5610.u2 5610v1 $$[1, 0, 1, -8, 278]$$ $$-47045881/33570240$$ $$-33570240$$ $$[2]$$ $$2304$$ $$0.12315$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.u

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 LMFDB 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 LMFDB labels.