# Properties

 Label 1110.e Number of curves $2$ Conductor $1110$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 1110.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.e1 1110g2 $$[1, 0, 1, -7089, -230588]$$ $$-39390416456458249/56832000000$$ $$-56832000000$$ $$[]$$ $$2160$$ $$0.96602$$
1110.e2 1110g1 $$[1, 0, 1, 126, -1484]$$ $$223759095911/1094104800$$ $$-1094104800$$ $$$$ $$720$$ $$0.41671$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1110.e have rank $$1$$.

## Complex multiplication

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

## Modular form1110.2.a.e

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 