Properties

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

Related objects

Downloads

Learn more

Show commands: 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 \([1, 0, 1, -320459, -14401618]\) \(3639478711331685826729/2016912141902025000\) \(2016912141902025000\) \([2]\) \(23040\) \(2.2028\)  
1110.g2 1110f2 \([1, 0, 1, -195459, 33048382]\) \(825824067562227826729/5613755625000000\) \(5613755625000000\) \([2, 2]\) \(11520\) \(1.8562\)  
1110.g3 1110f1 \([1, 0, 1, -195139, 33162686]\) \(821774646379511057449/38361600000\) \(38361600000\) \([2]\) \(5760\) \(1.5096\) \(\Gamma_0(N)\)-optimal
1110.g4 1110f4 \([1, 0, 1, -75579, 73184206]\) \(-47744008200656797609/2286529541015625000\) \(-2286529541015625000\) \([2]\) \(23040\) \(2.2028\)  

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 form 1110.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} + 2q^{13} - 4q^{14} - q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  Toggle raw display

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.