Properties

Label 144690.u
Number of curves $8$
Conductor $144690$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 144690.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144690.u1 144690bo7 \([1, 0, 1, -80723757524, 8826776804281322]\) \(58173851738883910269832957338271349689/7393016657522503991961739125000\) \(7393016657522503991961739125000\) \([2]\) \(796262400\) \(4.9450\)  
144690.u2 144690bo4 \([1, 0, 1, -80721295259, 8827342258883996]\) \(58168528582194364647795439498299413929/119424346138310850\) \(119424346138310850\) \([6]\) \(265420800\) \(4.3956\)  
144690.u3 144690bo8 \([1, 0, 1, -32031834244, -2116511967284374]\) \(3634704740957616196378170215513091769/168224880645019054412841796875000\) \(168224880645019054412841796875000\) \([2]\) \(796262400\) \(4.9450\)  
144690.u4 144690bo6 \([1, 0, 1, -5478132524, 112851857281322]\) \(18181148530782910620484886101349689/5019699469729676451890625000000\) \(5019699469729676451890625000000\) \([2, 2]\) \(398131200\) \(4.5984\)  
144690.u5 144690bo5 \([1, 0, 1, -5053231879, 137458871591252]\) \(14270243831786428793763519508616809/95578270312754001983224218750\) \(95578270312754001983224218750\) \([6]\) \(265420800\) \(4.3956\)  
144690.u6 144690bo2 \([1, 0, 1, -5045081009, 137926904327696]\) \(14201301386688072974887643602001929/643473293344889428102500\) \(643473293344889428102500\) \([2, 6]\) \(132710400\) \(4.0491\)  
144690.u7 144690bo1 \([1, 0, 1, -314808189, 2162398066312]\) \(-3450339047557525524160845096649/23342079353260249272927600\) \(-23342079353260249272927600\) \([6]\) \(66355200\) \(3.7025\) \(\Gamma_0(N)\)-optimal
144690.u8 144690bo3 \([1, 0, 1, 884325396, 11530987396906]\) \(76482135310664088565567458606791/101700066369522956078016000000\) \(-101700066369522956078016000000\) \([2]\) \(199065600\) \(4.2518\)  

Rank

sage: E.rank()
 

The elliptic curves in class 144690.u have rank \(0\).

Complex multiplication

The elliptic curves in class 144690.u do not have complex multiplication.

Modular form 144690.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} - q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 2 & 12 & 6 & 12 & 4 \\ 3 & 1 & 12 & 6 & 4 & 2 & 4 & 12 \\ 4 & 12 & 1 & 2 & 3 & 6 & 12 & 4 \\ 2 & 6 & 2 & 1 & 6 & 3 & 6 & 2 \\ 12 & 4 & 3 & 6 & 1 & 2 & 4 & 12 \\ 6 & 2 & 6 & 3 & 2 & 1 & 2 & 6 \\ 12 & 4 & 12 & 6 & 4 & 2 & 1 & 3 \\ 4 & 12 & 4 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.