Properties

Label 722.b
Number of curves 22
Conductor 722722
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 722.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
722.b1 722c2 [1,0,1,25278,1710222][1, 0, 1, -25278, 1710222] 37966934881/4952198-37966934881/4952198 232980517796438-232980517796438 [][] 36003600 1.49001.4900  
722.b2 722c1 [1,0,1,8,8138][1, 0, 1, -8, -8138] 1/608-1/608 28603895648-28603895648 [][] 720720 0.685290.68529 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 722.b have rank 00.

Complex multiplication

The elliptic curves in class 722.b do not have complex multiplication.

Modular form 722.2.a.b

sage: E.q_eigenform(10)
 
qq2+q3+q44q5q6+3q7q82q9+4q10+2q11+q12+q133q144q15+q16+3q17+2q18+O(q20)q - q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} + 3 q^{7} - q^{8} - 2 q^{9} + 4 q^{10} + 2 q^{11} + q^{12} + q^{13} - 3 q^{14} - 4 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 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 LMFDB numbering.

(1551)\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.