# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1110.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.g1 1110f3 $$[1, 0, 1, -320459, -14401618]$$ $$3639478711331685826729/2016912141902025000$$ $$2016912141902025000$$ $$$$ $$23040$$ $$2.2028$$
1110.g2 1110f2 $$[1, 0, 1, -195459, 33048382]$$ $$825824067562227826729/5613755625000000$$ $$5613755625000000$$ $$[2, 2]$$ $$11520$$ $$1.8562$$
1110.g3 1110f1 $$[1, 0, 1, -195139, 33162686]$$ $$821774646379511057449/38361600000$$ $$38361600000$$ $$$$ $$5760$$ $$1.5096$$ $$\Gamma_0(N)$$-optimal
1110.g4 1110f4 $$[1, 0, 1, -75579, 73184206]$$ $$-47744008200656797609/2286529541015625000$$ $$-2286529541015625000$$ $$$$ $$23040$$ $$2.2028$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1110.2.a.g

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 