# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 1122m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.j3 1122m1 $$[1, 0, 0, -205448, -35497920]$$ $$959024269496848362625/11151660319506432$$ $$11151660319506432$$ $$$$ $$11520$$ $$1.8916$$ $$\Gamma_0(N)$$-optimal
1122.j4 1122m2 $$[1, 0, 0, -41608, -90515392]$$ $$-7966267523043306625/3534510366354604032$$ $$-3534510366354604032$$ $$$$ $$23040$$ $$2.2382$$
1122.j1 1122m3 $$[1, 0, 0, -16594568, -26020768704]$$ $$505384091400037554067434625/815656731648$$ $$815656731648$$ $$$$ $$34560$$ $$2.4409$$
1122.j2 1122m4 $$[1, 0, 0, -16594408, -26021295520]$$ $$-505369473241574671219626625/20303219722982711328$$ $$-20303219722982711328$$ $$$$ $$69120$$ $$2.7875$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1122m do not have complex multiplication.

## Modular form1122.2.a.m

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 