# Properties

 Label 1122.l Number of curves $2$ Conductor $1122$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 1122.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.l1 1122j2 $$[1, 0, 0, -182, 930]$$ $$666940371553/37026$$ $$37026$$ $$[2]$$ $$192$$ $$-0.058012$$
1122.l2 1122j1 $$[1, 0, 0, -12, 12]$$ $$192100033/38148$$ $$38148$$ $$[2]$$ $$96$$ $$-0.40459$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1122.2.a.l

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.