# Properties

 Label 10830.i Number of curves $2$ Conductor $10830$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.i1 10830k2 $$[1, 0, 1, -26684, -1675654]$$ $$306331959547531/900000000$$ $$6173100000000$$ $$$$ $$61440$$ $$1.3244$$
10830.i2 10830k1 $$[1, 0, 1, -2364, -2438]$$ $$212883113611/122880000$$ $$842833920000$$ $$$$ $$30720$$ $$0.97786$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10830.i have rank $$0$$.

## Complex multiplication

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

## Modular form 10830.2.a.i

sage: E.q_eigenform(10)

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