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Properties

Label 1147.a
Number of curves $2$
Conductor $1147$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1147.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1147.a1 1147b2 \([0, -1, 1, -293560, -60546218]\) \(2797794606468551643136/30326246618289637\) \(30326246618289637\) \([]\) \(19600\) \(1.9778\)  
1147.a2 1147b1 \([0, -1, 1, -26790, 1696662]\) \(2126464142970105856/66639542677\) \(66639542677\) \([5]\) \(3920\) \(1.1731\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1147.a have rank \(1\).

Complex multiplication

The elliptic curves in class 1147.a do not have complex multiplication.

Modular form 1147.2.a.a

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.