# Properties

 Label 5610.a Number of curves $2$ Conductor $5610$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 5610.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.a1 5610c2 $$[1, 1, 0, -719108, -234128688]$$ $$41125104693338423360329/179205840000000000$$ $$179205840000000000$$ $$$$ $$99840$$ $$2.1636$$
5610.a2 5610c1 $$[1, 1, 0, -22788, -7267632]$$ $$-1308796492121439049/22000592486400000$$ $$-22000592486400000$$ $$$$ $$49920$$ $$1.8170$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.a

sage: E.q_eigenform(10)

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

## 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. 