# Properties

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

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 5610.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.i1 5610g2 $$[1, 1, 0, -185702, -30879084]$$ $$708234550511150304361/23696640000$$ $$23696640000$$ $$$$ $$28160$$ $$1.4903$$
5610.i2 5610g1 $$[1, 1, 0, -11622, -484716]$$ $$173629978755828841/1000026931200$$ $$1000026931200$$ $$$$ $$14080$$ $$1.1437$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5610.2.a.i

sage: E.q_eigenform(10)

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

## 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. 