# Properties

 Label 10830t Number of curves 2 Conductor 10830 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10830.s1")

sage: E.isogeny_class()

## Elliptic curves in class 10830t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.s1 10830t1 [1, 1, 1, -36, -111] [] 2592 $$\Gamma_0(N)$$-optimal
10830.s2 10830t2 [1, 1, 1, 249, 573] [] 7776

## Rank

sage: E.rank()

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

## Modular form 10830.2.a.s

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 