Properties

Label 20070.be
Number of curves 44
Conductor 2007020070
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 20070.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20070.be1 20070bg3 [1,1,1,757697342,7799122947891][1, -1, 1, -757697342, -7799122947891] 65990812340278189764070806169/214215063495877145491200065990812340278189764070806169/2142150634958771454912000 15616278128849443906308480001561627812884944390630848000 [2][2] 1107302411073024 3.99173.9917  
20070.be2 20070bg2 [1,1,1,115457342,308001020109][1, -1, 1, -115457342, 308001020109] 233486000400975208694166169/78913673205682176000000233486000400975208694166169/78913673205682176000000 5752806776694230630400000057528067766942306304000000 [2,2][2, 2] 55365125536512 3.64523.6452  
20070.be3 20070bg1 [1,1,1,103660862,406176045261][1, -1, 1, -103660862, 406176045261] 168982070711351853939176089/37703877214076928000168982070711351853939176089/37703877214076928000 2748612648906208051200027486126489062080512000 [4][4] 27682562768256 3.29863.2986 Γ0(N)\Gamma_0(N)-optimal
20070.be4 20070bg4 [1,1,1,338038978,2131781820621][1, -1, 1, 338038978, 2131781820621] 5859985279907178462243106151/60844420299003750000000005859985279907178462243106151/6084442029900375000000000 4435558239797373375000000000-4435558239797373375000000000 [2][2] 1107302411073024 3.99173.9917  

Rank

sage: E.rank()
 

The elliptic curves in class 20070.be have rank 00.

Complex multiplication

The elliptic curves in class 20070.be do not have complex multiplication.

Modular form 20070.2.a.be

sage: E.q_eigenform(10)
 
q+q2+q4+q5+q8+q104q112q13+q16+2q174q19+O(q20)q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4 q^{11} - 2 q^{13} + q^{16} + 2 q^{17} - 4 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 LMFDB numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.