# Properties

 Label 82800du Number of curves $6$ Conductor $82800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("82800.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 82800du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
82800.dl5 82800du1 [0, 0, 0, -1512075, 785160250] [2] 1769472 $$\Gamma_0(N)$$-optimal
82800.dl4 82800du2 [0, 0, 0, -24840075, 47651112250] [2, 2] 3538944
82800.dl3 82800du3 [0, 0, 0, -25488075, 45033840250] [2, 2] 7077888
82800.dl1 82800du4 [0, 0, 0, -397440075, 3049689312250] [2] 7077888
82800.dl6 82800du5 [0, 0, 0, 31643925, 218200932250] [2] 14155776
82800.dl2 82800du6 [0, 0, 0, -92988075, -295638659750] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 82800du have rank $$0$$.

## Modular form 82800.2.a.dl

sage: E.q_eigenform(10)

$$q + 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.