# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 1122.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.f1 1122f1 $$[1, 1, 1, -9, -9]$$ $$81182737/35904$$ $$35904$$ $$$$ $$96$$ $$-0.43024$$ $$\Gamma_0(N)$$-optimal
1122.f2 1122f2 $$[1, 1, 1, 31, -25]$$ $$3288008303/2517768$$ $$-2517768$$ $$$$ $$192$$ $$-0.083666$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 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. 