Properties

Label 20070.be
Number of curves $4$
Conductor $20070$
CM no
Rank $0$
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 \([1, -1, 1, -757697342, -7799122947891]\) \(65990812340278189764070806169/2142150634958771454912000\) \(1561627812884944390630848000\) \([2]\) \(11073024\) \(3.9917\)  
20070.be2 20070bg2 \([1, -1, 1, -115457342, 308001020109]\) \(233486000400975208694166169/78913673205682176000000\) \(57528067766942306304000000\) \([2, 2]\) \(5536512\) \(3.6452\)  
20070.be3 20070bg1 \([1, -1, 1, -103660862, 406176045261]\) \(168982070711351853939176089/37703877214076928000\) \(27486126489062080512000\) \([4]\) \(2768256\) \(3.2986\) \(\Gamma_0(N)\)-optimal
20070.be4 20070bg4 \([1, -1, 1, 338038978, 2131781820621]\) \(5859985279907178462243106151/6084442029900375000000000\) \(-4435558239797373375000000000\) \([2]\) \(11073024\) \(3.9917\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20070.be have rank \(0\).

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)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4 q^{11} - 2 q^{13} + q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.