Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 11760br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.b6 | 11760br1 | \([0, -1, 0, 7824, -375360]\) | \(109902239/188160\) | \(-90672479600640\) | \([2]\) | \(36864\) | \(1.3631\) | \(\Gamma_0(N)\)-optimal |
| 11760.b5 | 11760br2 | \([0, -1, 0, -54896, -3837504]\) | \(37966934881/8643600\) | \(4165267031654400\) | \([2, 2]\) | \(73728\) | \(1.7097\) | |
| 11760.b2 | 11760br3 | \([0, -1, 0, -823216, -287193920]\) | \(128031684631201/9922500\) | \(4781556541440000\) | \([2, 2]\) | \(147456\) | \(2.0563\) | |
| 11760.b4 | 11760br4 | \([0, -1, 0, -290096, 56938176]\) | \(5602762882081/345888060\) | \(166680102383370240\) | \([2]\) | \(147456\) | \(2.0563\) | |
| 11760.b1 | 11760br5 | \([0, -1, 0, -13171216, -18394301120]\) | \(524388516989299201/3150\) | \(1517954457600\) | \([2]\) | \(294912\) | \(2.4029\) | |
| 11760.b3 | 11760br6 | \([0, -1, 0, -768336, -327190464]\) | \(-104094944089921/35880468750\) | \(-17290449993600000000\) | \([2]\) | \(294912\) | \(2.4029\) |
Rank
sage: E.rank()
The elliptic curves in class 11760br have rank \(1\).
Complex multiplication
The elliptic curves in class 11760br do not have complex multiplication.Modular form 11760.2.a.br
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
