# Properties

 Label 4830.u Number of curves $2$ Conductor $4830$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 4830.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.u1 4830u1 $$[1, 1, 1, -112286, 14435483]$$ $$156567200830221067489/16905000000$$ $$16905000000$$ $$$$ $$17472$$ $$1.3894$$ $$\Gamma_0(N)$$-optimal
4830.u2 4830u2 $$[1, 1, 1, -112006, 14511419]$$ $$-155398856216042825569/1627294921875000$$ $$-1627294921875000$$ $$$$ $$34944$$ $$1.7360$$

## Rank

sage: E.rank()

The elliptic curves in class 4830.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4830.u do not have complex multiplication.

## Modular form4830.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - q^{12} + 6q^{13} + q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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. 