# Properties

 Label 1122k Number of curves $4$ Conductor $1122$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1122.m1")

sage: E.isogeny_class()

## Elliptic curves in class 1122k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.m4 1122k1 [1, 0, 0, -5847, -135063] [4] 2688 $$\Gamma_0(N)$$-optimal
1122.m2 1122k2 [1, 0, 0, -87767, -10014615] [2, 2] 5376
1122.m1 1122k3 [1, 0, 0, -1404247, -640608535] [2] 10752
1122.m3 1122k4 [1, 0, 0, -82007, -11384343] [2] 10752

## Rank

sage: E.rank()

The elliptic curves in class 1122k have rank $$0$$.

## Modular form1122.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + 4q^{7} + q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} - 2q^{13} + 4q^{14} + 2q^{15} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.