Properties

Label 266910v
Number of curves 22
Conductor 266910266910
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 266910v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266910.v1 266910v1 [1,0,1,16199,1098146][1, 0, 1, -16199, 1098146] 470056203380406889/250217962134840-470056203380406889/250217962134840 250217962134840-250217962134840 [3][3] 11793601179360 1.46681.4668 Γ0(N)\Gamma_0(N)-optimal
266910.v2 266910v2 [1,0,1,128386,14268688][1, 0, 1, 128386, -14268688] 234035413953867370151/223522342029504000234035413953867370151/223522342029504000 223522342029504000-223522342029504000 [][] 35380803538080 2.01612.0161  

Rank

sage: E.rank()
 

The elliptic curves in class 266910v have rank 00.

Complex multiplication

The elliptic curves in class 266910v do not have complex multiplication.

Modular form 266910.2.a.v

sage: E.q_eigenform(10)
 
qq2+q3+q4q5q6+q7q8+q9+q10+q12+2q13q14q15+q16q18+8q19+O(q20)q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + 2 q^{13} - q^{14} - q^{15} + q^{16} - q^{18} + 8 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.