Properties

Label 266910.ck
Number of curves 8
Conductor \(266910\)
CM no
Rank \(1\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("266910.ck1")
sage: E.isogeny_class()

Elliptic curves in class 266910.ck

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
266910.ck1 266910ck8 [1, 0, 0, -9320773825040, -10952689658836929780L] 2 13287555072  
266910.ck2 266910ck3 [1, 0, 0, -2178935510140, 1237982811464867600] 8 3321888768  
266910.ck3 266910ck6 [1, 0, 0, -599206392140, -160829690671372800] 4 6643777536  
266910.ck4 266910ck4 [1, 0, 0, -141433110140, 17771562402147600] 8 3321888768  
266910.ck5 266910ck2 [1, 0, 0, -136184310140, 19343222133507600] 16 1660944384  
266910.ck6 266910ck1 [1, 0, 0, -8184310140, 326543733507600] 8 830472192 \(\Gamma_0(N)\)-optimal
266910.ck7 266910ck5 [1, 0, 0, 232359371860, 95786613663828000] 4 6643777536  
266910.ck8 266910ck7 [1, 0, 0, 797988528760, -799448088117993420] 2 13287555072  

Rank

sage: E.rank()

The elliptic curves in class 266910.ck have rank \(1\).

Modular form 266910.2.1.ck

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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