# Properties

 Label 1122f Number of curves $2$ Conductor $1122$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1122.f1")

sage: E.isogeny_class()

## Elliptic curves in class 1122f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.f1 1122f1 [1, 1, 1, -9, -9]  96 $$\Gamma_0(N)$$-optimal
1122.f2 1122f2 [1, 1, 1, 31, -25]  192

## Rank

sage: E.rank()

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

## Modular form1122.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 