Properties

Label 106560bh
Number of curves 22
Conductor 106560106560
CM no
Rank 00
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bh1") E.isogeny_class()
 

Elliptic curves in class 106560bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106560.be2 106560bh1 [0,0,0,6528,78752][0, 0, 0, -6528, 78752] 2575826944/12663252575826944/1266325 1512490475520015124904755200 [][] 138240138240 1.22221.2222 Γ0(N)\Gamma_0(N)-optimal
106560.be1 106560bh2 [0,0,0,432768,109579808][0, 0, 0, -432768, 109579808] 750484394082304/578125750484394082304/578125 69050880000006905088000000 [][] 414720414720 1.77151.7715  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 106560bh have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
551+T1 + T
37371+T1 + T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 1+T+7T2 1 + T + 7 T^{2} 1.7.b
1111 13T+11T2 1 - 3 T + 11 T^{2} 1.11.ad
1313 1+2T+13T2 1 + 2 T + 13 T^{2} 1.13.c
1717 1+3T+17T2 1 + 3 T + 17 T^{2} 1.17.d
1919 1+2T+19T2 1 + 2 T + 19 T^{2} 1.19.c
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 1+3T+29T2 1 + 3 T + 29 T^{2} 1.29.d
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 106560bh do not have complex multiplication.

Modular form 106560.2.a.bh

Copy content sage:E.q_eigenform(10)
 
qq5q73q11+4q13+4q19+O(q20)q - q^{5} - q^{7} - 3 q^{11} + 4 q^{13} + 4 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.