Properties

Label 107800.bd
Number of curves 22
Conductor 107800107800
CM no
Rank 00
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bd1") E.isogeny_class()
 

Elliptic curves in class 107800.bd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
107800.bd1 107800cg1 [0,0,0,5635,154350][0, 0, 0, -5635, 154350] 1314036/771314036/77 11595485440001159548544000 [2][2] 9830498304 1.06841.0684 Γ0(N)\Gamma_0(N)-optimal
107800.bd2 107800cg2 [0,0,0,4165,634550][0, 0, 0, 4165, 634550] 265302/5929265302/5929 178570475776000-178570475776000 [2][2] 196608196608 1.41491.4149  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 107800.bd have rank 00.

Complex multiplication

The elliptic curves in class 107800.bd do not have complex multiplication.

Modular form 107800.2.a.bd

Copy content sage:E.q_eigenform(10)
 
q3q9q112q13+4q19+O(q20)q - 3 q^{9} - q^{11} - 2 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 LMFDB numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.