# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 10830n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.o2 10830n1 $$[1, 0, 1, -293, 1856]$$ $$403583419/10800$$ $$74077200$$ $$$$ $$3840$$ $$0.29078$$ $$\Gamma_0(N)$$-optimal
10830.o1 10830n2 $$[1, 0, 1, -673, -4072]$$ $$4904335099/1822500$$ $$12500527500$$ $$$$ $$7680$$ $$0.63735$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.n

sage: E.q_eigenform(10)

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