One refined passport of genus 15 with automorphism group $C_2$

• Label: 15.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(C_2\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$C_2$
Group identifier:	$[2,1]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$

Conjugacy classes for this refined passport:

$2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2$

Jacobian variety group algebra decomposition:

$A_{15}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,2)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{30}+a_{1}x^{29}+a_{2}x^{28}+a_{3}x^{27}+a_{4}x^{26}+a_{5}x^{25}+a_{6}x^{24}+a_{7}x^{23}+a_{8}x^{22}+a_{9}x^{21}+a_{10}x^{20}+a_{11}x^{19}+a_{12}x^{18}+a_{13}x^{17}+a_{14}x^{16}+a_{15}x^{15}+a_{16}x^{14}+a_{17}x^{13}+a_{18}x^{12}+a_{19}x^{11}+a_{20}x^{10}+a_{21}x^{9}+a_{22}x^{8}+a_{23}x^{7}+a_{24}x^{6}+a_{25}x^{5}+a_{26}x^{4}+a_{27}x^{3}+a_{28}x^{2}+a_{29}x + 1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1.1

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