Properties

Label 1110.e
Number of curves $2$
Conductor $1110$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1110.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.e1 1110g2 \([1, 0, 1, -7089, -230588]\) \(-39390416456458249/56832000000\) \(-56832000000\) \([]\) \(2160\) \(0.96602\)  
1110.e2 1110g1 \([1, 0, 1, 126, -1484]\) \(223759095911/1094104800\) \(-1094104800\) \([3]\) \(720\) \(0.41671\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1110.e have rank \(1\).

Complex multiplication

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

Modular form 1110.2.a.e

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.