# Properties

 Label 2730.bd Number of curves 8 Conductor 2730 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2730.bd1")
sage: E.isogeny_class()

## Elliptic curves in class 2730.bd

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2730.bd1 2730bd7 [1, 0, 0, -40190455, -98072518885] 2 110592
2730.bd2 2730bd6 [1, 0, 0, -2511905, -1532538075] 4 55296
2730.bd3 2730bd8 [1, 0, 0, -2481035, -1572033153] 2 110592
2730.bd4 2730bd4 [1, 0, 0, -496405, -134437975] 6 36864
2730.bd5 2730bd3 [1, 0, 0, -158925, -23336703] 4 27648
2730.bd6 2730bd2 [1, 0, 0, -41405, -576975] 12 18432
2730.bd7 2730bd1 [1, 0, 0, -25725, 1577457] 12 9216 $$\Gamma_0(N)$$-optimal
2730.bd8 2730bd5 [1, 0, 0, 162715, -4536903] 6 36864

## Rank

sage: E.rank()

The elliptic curves in class 2730.bd have rank $$0$$.

## Modular form2730.2.a.bd

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.