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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 203280.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.cu1 | 203280cy8 | \([0, -1, 0, -3718668840, -87281701302288]\) | \(783736670177727068275201/360150\) | \(2613361435238400\) | \([2]\) | \(62914560\) | \(3.6865\) | |
| 203280.cu2 | 203280cy6 | \([0, -1, 0, -232416840, -1363718012688]\) | \(191342053882402567201/129708022500\) | \(941202120901109760000\) | \([2, 2]\) | \(31457280\) | \(3.3400\) | |
| 203280.cu3 | 203280cy7 | \([0, -1, 0, -230964840, -1381599683088]\) | \(-187778242790732059201/4984939585440150\) | \(-36172286185152256303718400\) | \([2]\) | \(62914560\) | \(3.6865\) | |
| 203280.cu4 | 203280cy3 | \([0, -1, 0, -29175560, 60649474800]\) | \(378499465220294881/120530818800\) | \(874609450533465292800\) | \([2]\) | \(15728640\) | \(2.9934\) | |
| 203280.cu5 | 203280cy4 | \([0, -1, 0, -14616840, -21024572688]\) | \(47595748626367201/1215506250000\) | \(8820094843929600000000\) | \([2, 2]\) | \(15728640\) | \(2.9934\) | |
| 203280.cu6 | 203280cy2 | \([0, -1, 0, -2071560, 673743600]\) | \(135487869158881/51438240000\) | \(373252013640253440000\) | \([2, 2]\) | \(7864320\) | \(2.6468\) | |
| 203280.cu7 | 203280cy1 | \([0, -1, 0, 406520, 75039472]\) | \(1023887723039/928972800\) | \(-6740918200487116800\) | \([2]\) | \(3932160\) | \(2.3002\) | \(\Gamma_0(N)\)-optimal |
| 203280.cu8 | 203280cy5 | \([0, -1, 0, 2458680, -67224099600]\) | \(226523624554079/269165039062500\) | \(-1953146002500000000000000\) | \([2]\) | \(31457280\) | \(3.3400\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.cu do not have complex multiplication.Modular form 203280.2.a.cu
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
