# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1122.a1")

sage: E.isogeny_class()

## Elliptic curves in class 1122c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.a4 1122c1 [1, 1, 0, -6666, 154836]  2688 $$\Gamma_0(N)$$-optimal
1122.a2 1122c2 [1, 1, 0, -99146, 11973780] [2, 2] 5376
1122.a1 1122c3 [1, 1, 0, -1586306, 768343356]  10752
1122.a3 1122c4 [1, 1, 0, -91666, 13866220]  10752

## Rank

sage: E.rank()

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

## Modular form1122.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 