# Properties

 Label 28830bd Number of curves $6$ Conductor $28830$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28830.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 28830bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28830.bf6 28830bd1 [1, 1, 1, 57640, 30202265] [4] 491520 $$\Gamma_0(N)$$-optimal
28830.bf5 28830bd2 [1, 1, 1, -1172440, 461222297] [2, 2] 983040
28830.bf4 28830bd3 [1, 1, 1, -3555720, -2013575655] [2] 1966080
28830.bf2 28830bd4 [1, 1, 1, -18470440, 30545903897] [2, 2] 1966080
28830.bf3 28830bd5 [1, 1, 1, -18182140, 31545958937] [2] 3932160
28830.bf1 28830bd6 [1, 1, 1, -295526740, 1955311431257] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 28830bd have rank $$0$$.

## Modular form 28830.2.a.bf

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} - 6q^{13} - q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.