# Properties

 Label 22800dk Number of curves $4$ Conductor $22800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22800.dt1")

sage: E.isogeny_class()

## Elliptic curves in class 22800dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22800.dt4 22800dk1 [0, 1, 0, -4008, -168012] [2] 55296 $$\Gamma_0(N)$$-optimal
22800.dt3 22800dk2 [0, 1, 0, -76008, -8088012] [2, 2] 110592
22800.dt2 22800dk3 [0, 1, 0, -88008, -5376012] [2] 221184
22800.dt1 22800dk4 [0, 1, 0, -1216008, -516528012] [2] 221184

## Rank

sage: E.rank()

The elliptic curves in class 22800dk have rank $$0$$.

## Modular form 22800.2.a.dt

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} + 4q^{11} + 2q^{13} + 2q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.