# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1110.e1")

sage: E.isogeny_class()

## Elliptic curves in class 1110g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.e2 1110g1 [1, 0, 1, 126, -1484]  720 $$\Gamma_0(N)$$-optimal
1110.e1 1110g2 [1, 0, 1, -7089, -230588] [] 2160

## Rank

sage: E.rank()

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

## 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 Cremona 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 Cremona labels. 