# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1122.c1")

sage: E.isogeny_class()

## Elliptic curves in class 1122.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.c1 1122b3 [1, 1, 0, -483939, 129374577]  15360
1122.c2 1122b2 [1, 1, 0, -31399, 1848805] [2, 2] 7680
1122.c3 1122b1 [1, 1, 0, -8279, -264363]  3840 $$\Gamma_0(N)$$-optimal
1122.c4 1122b4 [1, 1, 0, 51221, 10028185]  15360

## Rank

sage: E.rank()

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

## Modular form1122.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 