# Properties

 Label 4830bc Number of curves 8 Conductor 4830 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4830.be1")

sage: E.isogeny_class()

## Elliptic curves in class 4830bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4830.be7 4830bc1 [1, 0, 0, -3082736, -2078064384] [6] 165888 $$\Gamma_0(N)$$-optimal
4830.be6 4830bc2 [1, 0, 0, -4393456, -140558080] [2, 6] 331776
4830.be3 4830bc3 [1, 0, 0, -249518576, -1517079678720] [2] 497664
4830.be5 4830bc4 [1, 0, 0, -47316976, 124844147456] [6] 663552
4830.be8 4830bc5 [1, 0, 0, 17558544, -1119617280] [6] 663552
4830.be2 4830bc6 [1, 0, 0, -249518896, -1517075593024] [2, 2] 995328
4830.be1 4830bc7 [1, 0, 0, -253899016, -1461052982200] [2] 1990656
4830.be4 4830bc8 [1, 0, 0, -245143896, -1572836718024] [2] 1990656

## Rank

sage: E.rank()

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

## Modular form4830.2.a.be

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.