# Properties

 Label 1122m Number of curves $4$ Conductor $1122$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1122.j1")

sage: E.isogeny_class()

## Elliptic curves in class 1122m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.j3 1122m1 [1, 0, 0, -205448, -35497920]  11520 $$\Gamma_0(N)$$-optimal
1122.j4 1122m2 [1, 0, 0, -41608, -90515392]  23040
1122.j1 1122m3 [1, 0, 0, -16594568, -26020768704]  34560
1122.j2 1122m4 [1, 0, 0, -16594408, -26021295520]  69120

## Rank

sage: E.rank()

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

## Modular form1122.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 