# Properties

 Label 10830t Number of curves $2$ Conductor $10830$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 10830t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.s1 10830t1 $$[1, 1, 1, -36, -111]$$ $$-14317849/2700$$ $$-974700$$ $$[]$$ $$2592$$ $$-0.12672$$ $$\Gamma_0(N)$$-optimal
10830.s2 10830t2 $$[1, 1, 1, 249, 573]$$ $$4728305591/3000000$$ $$-1083000000$$ $$[]$$ $$7776$$ $$0.42258$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.t

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.