Properties

Label 158d
Number of curves 33
Conductor 158158
CM no
Rank 00
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 158d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158.b2 158d1 [1,0,1,82,92][1, 0, 1, -82, -92] 59914169497/3155449659914169497/31554496 3155449631554496 [3][3] 4040 0.130550.13055 Γ0(N)\Gamma_0(N)-optimal
158.b1 158d2 [1,0,1,5217,145452][1, 0, 1, -5217, -145452] 15698803397448457/2070937615698803397448457/20709376 2070937620709376 [][] 120120 0.679860.67986  
158.b3 158d3 [1,0,1,47,118][1, 0, 1, -47, 118] 11134383337/31611134383337/316 316316 [3][3] 120120 0.41875-0.41875  

Rank

sage: E.rank()
 

The elliptic curves in class 158d have rank 00.

Complex multiplication

The elliptic curves in class 158d do not have complex multiplication.

Modular form 158.2.a.d

sage: E.q_eigenform(10)
 
qq2+q3+q4+3q5q6q7q82q93q10+q12+5q13+q14+3q15+q16+2q18+2q19+O(q20)q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} - 2 q^{9} - 3 q^{10} + q^{12} + 5 q^{13} + q^{14} + 3 q^{15} + q^{16} + 2 q^{18} + 2 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.

(133319391)\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.