# Properties

 Label 1110.h Number of curves $4$ Conductor $1110$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1110.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.h1 1110h4 $$[1, 0, 1, -10488, -185402]$$ $$127568139540190201/59114336463360$$ $$59114336463360$$ $$$$ $$6048$$ $$1.3371$$
1110.h2 1110h2 $$[1, 0, 1, -5313, 148588]$$ $$16581570075765001/998001000$$ $$998001000$$ $$$$ $$2016$$ $$0.78784$$
1110.h3 1110h1 $$[1, 0, 1, -313, 2588]$$ $$-3375675045001/999000000$$ $$-999000000$$ $$$$ $$1008$$ $$0.44126$$ $$\Gamma_0(N)$$-optimal
1110.h4 1110h3 $$[1, 0, 1, 2312, -21562]$$ $$1367594037332999/995878502400$$ $$-995878502400$$ $$$$ $$3024$$ $$0.99057$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1110.h do not have complex multiplication.

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 