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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28560.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.j1 | 28560cd7 | \([0, -1, 0, -212797856, 1193995846656]\) | \(260174968233082037895439009/223081361502731896500\) | \(913741256715189848064000\) | \([2]\) | \(5308416\) | \(3.5244\) | |
| 28560.j2 | 28560cd8 | \([0, -1, 0, -139757856, -629148409344]\) | \(73704237235978088924479009/899277423164136103500\) | \(3683440325280301479936000\) | \([2]\) | \(5308416\) | \(3.5244\) | |
| 28560.j3 | 28560cd5 | \([0, -1, 0, -139346016, -633079261440]\) | \(73054578035931991395831649/136386452160\) | \(558638908047360\) | \([2]\) | \(1769472\) | \(2.9751\) | |
| 28560.j4 | 28560cd6 | \([0, -1, 0, -16277856, 9687718656]\) | \(116454264690812369959009/57505157319440250000\) | \(235541124380427264000000\) | \([2, 2]\) | \(2654208\) | \(3.1778\) | |
| 28560.j5 | 28560cd4 | \([0, -1, 0, -9144416, -8846035200]\) | \(20645800966247918737249/3688936444974392640\) | \(15109883678615112253440\) | \([2]\) | \(1769472\) | \(2.9751\) | |
| 28560.j6 | 28560cd2 | \([0, -1, 0, -8709216, -9889470720]\) | \(17836145204788591940449/770635366502400\) | \(3156522461193830400\) | \([2, 2]\) | \(884736\) | \(2.6285\) | |
| 28560.j7 | 28560cd1 | \([0, -1, 0, -517216, -170481920]\) | \(-3735772816268612449/909650165760000\) | \(-3725927078952960000\) | \([2]\) | \(442368\) | \(2.2819\) | \(\Gamma_0(N)\)-optimal |
| 28560.j8 | 28560cd3 | \([0, -1, 0, 3722144, 1159718656]\) | \(1392333139184610040991/947901937500000000\) | \(-3882606336000000000000\) | \([2]\) | \(1327104\) | \(2.8312\) |
Rank
sage: E.rank()
The elliptic curves in class 28560.j have rank \(0\).
Complex multiplication
The elliptic curves in class 28560.j do not have complex multiplication.Modular form 28560.2.a.j
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
