# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1122.h1")

sage: E.isogeny_class()

## Elliptic curves in class 1122.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.h1 1122h3 [1, 1, 1, -1937, -31219]  1536
1122.h2 1122h2 [1, 1, 1, -407, 2441] [2, 2] 768
1122.h3 1122h1 [1, 1, 1, -387, 2769]  384 $$\Gamma_0(N)$$-optimal
1122.h4 1122h4 [1, 1, 1, 803, 15509]  1536

## Rank

sage: E.rank()

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

## Modular form1122.2.a.h

sage: E.q_eigenform(10)

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

## 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. 