Properties

Label 10626.p
Number of curves $6$
Conductor $10626$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10626.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.p1 10626r5 \([1, 0, 0, -68877094, -220024810702]\) \(36136672427711016379227705697/1011258101510224722\) \(1011258101510224722\) \([2]\) \(819200\) \(2.9656\)  
10626.p2 10626r4 \([1, 0, 0, -4929124, 4203486548]\) \(13244420128496241770842177/29965867631164664892\) \(29965867631164664892\) \([4]\) \(409600\) \(2.6190\)  
10626.p3 10626r3 \([1, 0, 0, -4310284, -3428989876]\) \(8856076866003496152467137/46664863048067576004\) \(46664863048067576004\) \([2, 2]\) \(409600\) \(2.6190\)  
10626.p4 10626r6 \([1, 0, 0, -1977394, -7125687370]\) \(-855073332201294509246497/21439133060285771735058\) \(-21439133060285771735058\) \([2]\) \(819200\) \(2.9656\)  
10626.p5 10626r2 \([1, 0, 0, -420664, 13323824]\) \(8232463578739844255617/4687062591766850064\) \(4687062591766850064\) \([2, 4]\) \(204800\) \(2.2724\)  
10626.p6 10626r1 \([1, 0, 0, 104216, 1671488]\) \(125177609053596564863/73635189229502208\) \(-73635189229502208\) \([8]\) \(102400\) \(1.9259\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10626.p have rank \(0\).

Complex multiplication

The elliptic curves in class 10626.p do not have complex multiplication.

Modular form 10626.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.