# Properties

 Label 1110.i Number of curves $2$ Conductor $1110$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 1110.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.i1 1110i2 $$[1, 1, 1, -21146, -1192057]$$ $$1045706191321645729/323352324000$$ $$323352324000$$ $$$$ $$2400$$ $$1.1850$$
1110.i2 1110i1 $$[1, 1, 1, -1146, -24057]$$ $$-166456688365729/143856000000$$ $$-143856000000$$ $$$$ $$1200$$ $$0.83841$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1110.2.a.i

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 