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Properties

Label 6006.i
Number of curves $2$
Conductor $6006$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 6006.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6006.i1 6006f2 \([1, 1, 0, -12183, -521115]\) \(200005594092187129/704174238768\) \(704174238768\) \([2]\) \(24576\) \(1.1356\)  
6006.i2 6006f1 \([1, 1, 0, -423, -15435]\) \(-8401330071289/95718534912\) \(-95718534912\) \([2]\) \(12288\) \(0.78901\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6006.i have rank \(0\).

Complex multiplication

The elliptic curves in class 6006.i do not have complex multiplication.

Modular form 6006.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.