Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.h1 1110h4 \([1, 0, 1, -10488, -185402]\) \(127568139540190201/59114336463360\) \(59114336463360\) \([2]\) \(6048\) \(1.3371\)  
1110.h2 1110h2 \([1, 0, 1, -5313, 148588]\) \(16581570075765001/998001000\) \(998001000\) \([6]\) \(2016\) \(0.78784\)  
1110.h3 1110h1 \([1, 0, 1, -313, 2588]\) \(-3375675045001/999000000\) \(-999000000\) \([6]\) \(1008\) \(0.44126\) \(\Gamma_0(N)\)-optimal
1110.h4 1110h3 \([1, 0, 1, 2312, -21562]\) \(1367594037332999/995878502400\) \(-995878502400\) \([2]\) \(3024\) \(0.99057\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1110.h have rank \(0\).

Complex multiplication

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

Modular form 1110.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + 6q^{11} + q^{12} + 2q^{13} + 4q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.