Properties

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

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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 \([1, 1, 1, -21146, -1192057]\) \(1045706191321645729/323352324000\) \(323352324000\) \([2]\) \(2400\) \(1.1850\)  
1110.i2 1110i1 \([1, 1, 1, -1146, -24057]\) \(-166456688365729/143856000000\) \(-143856000000\) \([2]\) \(1200\) \(0.83841\) \(\Gamma_0(N)\)-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 form 1110.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 2q^{11} - q^{12} - 2q^{13} + q^{15} + q^{16} + 6q^{17} + q^{18} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.