Properties

Label 107800bu
Number of curves 22
Conductor 107800107800
CM no
Rank 11
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bu1") E.isogeny_class()
 

Elliptic curves in class 107800bu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
107800.g2 107800bu1 [0,1,0,408,3426688][0, 1, 0, -408, 3426688] 4/2695-4/2695 5073024880000000-5073024880000000 [2][2] 589824589824 1.69241.6924 Γ0(N)\Gamma_0(N)-optimal
107800.g1 107800bu2 [0,1,0,343408,76142688][0, 1, 0, -343408, 76142688] 1189646642/211751189646642/21175 7971896240000000079718962400000000 [2][2] 11796481179648 2.03902.0390  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 107800bu have rank 11.

Complex multiplication

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

Modular form 107800.2.a.bu

Copy content sage:E.q_eigenform(10)
 
q2q3+q9q11+6q13+2q172q19+O(q20)q - 2 q^{3} + q^{9} - q^{11} + 6 q^{13} + 2 q^{17} - 2 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.

(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 Cremona labels.