# Properties

 Label 10830.d Number of curves $2$ Conductor $10830$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.d1 10830d2 $$[1, 1, 0, -8420693, 9401731647]$$ $$1403607530712116449/39475350$$ $$1857152618533350$$ $$$$ $$403200$$ $$2.4403$$
10830.d2 10830d1 $$[1, 1, 0, -525623, 147130593]$$ $$-341370886042369/1817528220$$ $$-85507216352261820$$ $$$$ $$201600$$ $$2.0937$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.d

sage: E.q_eigenform(10)

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