# Properties

 Label 10830.k Number of curves $4$ Conductor $10830$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.k1 10830l3 $$[1, 0, 1, -224189, 40779086]$$ $$26487576322129/44531250$$ $$2095011888281250$$ $$[2]$$ $$92160$$ $$1.8351$$
10830.k2 10830l2 $$[1, 0, 1, -18419, 201242]$$ $$14688124849/8122500$$ $$382130168422500$$ $$[2, 2]$$ $$46080$$ $$1.4886$$
10830.k3 10830l1 $$[1, 0, 1, -11199, -454334]$$ $$3301293169/22800$$ $$1072646086800$$ $$[2]$$ $$23040$$ $$1.1420$$ $$\Gamma_0(N)$$-optimal
10830.k4 10830l4 $$[1, 0, 1, 71831, 1609142]$$ $$871257511151/527800050$$ $$-24830818344094050$$ $$[2]$$ $$92160$$ $$1.8351$$

## Rank

sage: E.rank()

The elliptic curves in class 10830.k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 10830.k do not have complex multiplication.

## Modular form 10830.2.a.k

sage: E.q_eigenform(10)

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

## 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.