# Properties

 Label 284592eu Number of curves 6 Conductor 284592 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("284592.eu1")

sage: E.isogeny_class()

## Elliptic curves in class 284592eu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
284592.eu4 284592eu1 [0, -1, 0, -3227352, -2229814992] [2] 7372800 $$\Gamma_0(N)$$-optimal
284592.eu3 284592eu2 [0, -1, 0, -3701672, -1530857040] [2, 2] 14745600
284592.eu2 284592eu3 [0, -1, 0, -26943352, 52761707440] [2, 2] 29491200
284592.eu6 284592eu4 [0, -1, 0, 11950888, -11097701712] [2] 29491200
284592.eu1 284592eu5 [0, -1, 0, -428692392, 3416526069552] [2] 58982400
284592.eu5 284592eu6 [0, -1, 0, 2938808, 163349605168] [2] 58982400

## Rank

sage: E.rank()

The elliptic curves in class 284592eu have rank $$0$$.

## Modular form 284592.2.a.eu

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} + 6q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.