# Properties

 Label 4410.n Number of curves $2$ Conductor $4410$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4410.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.n1 4410q1 $$[1, -1, 0, -6624, -77652]$$ $$1092727/540$$ $$15885600931620$$ $$$$ $$10752$$ $$1.2261$$ $$\Gamma_0(N)$$-optimal
4410.n2 4410q2 $$[1, -1, 0, 24246, -614790]$$ $$53582633/36450$$ $$-1072278062884350$$ $$$$ $$21504$$ $$1.5727$$

## Rank

sage: E.rank()

The elliptic curves in class 4410.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4410.n do not have complex multiplication.

## Modular form4410.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2 q^{11} - 2 q^{13} + q^{16} - 4 q^{17} + O(q^{20})$$

## 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. 