# Properties

 Label 10830.k Number of curves 4 Conductor 10830 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10830.k1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.k1 10830l3 [1, 0, 1, -224189, 40779086]  92160
10830.k2 10830l2 [1, 0, 1, -18419, 201242] [2, 2] 46080
10830.k3 10830l1 [1, 0, 1, -11199, -454334]  23040 $$\Gamma_0(N)$$-optimal
10830.k4 10830l4 [1, 0, 1, 71831, 1609142]  92160

## Rank

sage: E.rank()

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

## 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. 