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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)
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.