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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 203280j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.hb6 | 203280j1 | \([0, 1, 0, 19320, -1440012]\) | \(109902239/188160\) | \(-1365348015144960\) | \([2]\) | \(983040\) | \(1.5891\) | \(\Gamma_0(N)\)-optimal |
| 203280.hb5 | 203280j2 | \([0, 1, 0, -135560, -15007500]\) | \(37966934881/8643600\) | \(62720674445721600\) | \([2, 2]\) | \(1966080\) | \(1.9357\) | |
| 203280.hb4 | 203280j3 | \([0, 1, 0, -716360, 220332660]\) | \(5602762882081/345888060\) | \(2509872322402959360\) | \([2]\) | \(3932160\) | \(2.2823\) | |
| 203280.hb2 | 203280j4 | \([0, 1, 0, -2032840, -1116188812]\) | \(128031684631201/9922500\) | \(72000774236160000\) | \([2, 2]\) | \(3932160\) | \(2.2823\) | |
| 203280.hb3 | 203280j5 | \([0, 1, 0, -1897320, -1271277900]\) | \(-104094944089921/35880468750\) | \(-260359942550400000000\) | \([2]\) | \(7864320\) | \(2.6289\) | |
| 203280.hb1 | 203280j6 | \([0, 1, 0, -32524840, -71406347212]\) | \(524388516989299201/3150\) | \(22857388646400\) | \([2]\) | \(7864320\) | \(2.6289\) |
Rank
sage: E.rank()
The elliptic curves in class 203280j have rank \(0\).
Complex multiplication
The elliptic curves in class 203280j do not have complex multiplication.Modular form 203280.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
