# Properties

 Label 1122i Number of curves $2$ Conductor $1122$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1122.i1")

sage: E.isogeny_class()

## Elliptic curves in class 1122i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.i1 1122i1 [1, 0, 0, -904, 10304] [2] 1120 $$\Gamma_0(N)$$-optimal
1122.i2 1122i2 [1, 0, 0, -264, 24768] [2] 2240

## Rank

sage: E.rank()

The elliptic curves in class 1122i have rank $$1$$.

## Modular form1122.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.