# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("10830.g1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.g1 10830g4 [1, 1, 0, -19069263652, 1013550971091124]  8640000
10830.g2 10830g3 [1, 1, 0, -1191828872, 15836364428016]  4320000
10830.g3 10830g2 [1, 1, 0, -31748152, 59307836224]  1728000
10830.g4 10830g1 [1, 1, 0, 3369928, 5064449856]  864000 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 10830.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 