# Properties

 Label 10830.z Number of curves $2$ Conductor $10830$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10830.z1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.z1 10830bb2 [1, 0, 0, -25781, 1590945]  20480
10830.z2 10830bb1 [1, 0, 0, -1461, 29601]  10240 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 10830.2.a.z

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 