Properties

Label 966.g
Number of curves $6$
Conductor $966$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.g1 966g5 \([1, 1, 1, -79134, -8601153]\) \(54804145548726848737/637608031452\) \(637608031452\) \([2]\) \(4096\) \(1.4160\)  
966.g2 966g4 \([1, 1, 1, -17714, 900047]\) \(614716917569296417/19093020912\) \(19093020912\) \([8]\) \(2048\) \(1.0694\)  
966.g3 966g3 \([1, 1, 1, -5074, -128689]\) \(14447092394873377/1439452851984\) \(1439452851984\) \([2, 2]\) \(2048\) \(1.0694\)  
966.g4 966g2 \([1, 1, 1, -1154, 12431]\) \(169967019783457/26337394944\) \(26337394944\) \([2, 4]\) \(1024\) \(0.72283\)  
966.g5 966g1 \([1, 1, 1, 126, 1167]\) \(221115865823/664731648\) \(-664731648\) \([4]\) \(512\) \(0.37625\) \(\Gamma_0(N)\)-optimal
966.g6 966g6 \([1, 1, 1, 6266, -609505]\) \(27207619911317663/177609314617308\) \(-177609314617308\) \([2]\) \(4096\) \(1.4160\)  

Rank

sage: E.rank()
 

The elliptic curves in class 966.g have rank \(1\).

Complex multiplication

The elliptic curves in class 966.g do not have complex multiplication.

Modular form 966.2.a.g

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.