# Properties

 Label 1110h Number of curves $4$ Conductor $1110$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1110.h1")

sage: E.isogeny_class()

## Elliptic curves in class 1110h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.h3 1110h1 [1, 0, 1, -313, 2588] [6] 1008 $$\Gamma_0(N)$$-optimal
1110.h2 1110h2 [1, 0, 1, -5313, 148588] [6] 2016
1110.h4 1110h3 [1, 0, 1, 2312, -21562] [2] 3024
1110.h1 1110h4 [1, 0, 1, -10488, -185402] [2] 6048

## Rank

sage: E.rank()

The elliptic curves in class 1110h have rank $$0$$.

## Modular form1110.2.a.h

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.