Passport 7T7-6.1_5.2_4.2.1

• Label: 7T7-6.1_5.2_4.2.1
• Group: 7T7
• Orders: [6, 10, 4]
• Genus: 1
• Size: 21
• Galois orbits: 1

Passport invariants

Degree:	$7$
Monodromy group:	$S_7$
Genus:	$1$
Geometry type:	hyperbolic
Primitive:	yes

Conjugacy class data

The order and cycle type of an element in each of the conjugacy classes $C_0, C_1, C_{\infty}$ of the passport containing this orbit.

Order	Partition
$6$	$6, 1$
$10$	$5, 2$
$4$	$4, 2, 1$

Galois orbits

Passport size:		$21$
Number of Galois orbits:		$1$

Label	Orbit size	Base field	Representative triple
a	$21$	\(\mathbb{Q}(\nu)\); Generator \(\nu\), with minimal polynomial $x^{21} - 3 x^{20} + 3 x^{19} + x^{18} + 48 x^{17} + 240 x^{16} - 643 x^{15} - 3897 x^{14} + 9309 x^{13} + 32213 x^{12} - 43716 x^{11} + 53556 x^{10} - 391371 x^{9} + 25269 x^{8} - 216351 x^{7} + 653291 x^{6} + 657450 x^{5} - 58410 x^{4} - 604625 x^{3} - 243435 x^{2} + 49425 x + 26765$.	$(1,2,3,4,5,7),(1,3)(2,7,5,6,4),(1,2,3,4)(5,6)$