Genus 2 curves in isogeny class 17689.e of discriminant 866761

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Label	Class	Conductor	Discriminant	Rank*	2-Selmer rank	Torsion	$\textrm{End}^0(J_{\overline\Q})$	$\textrm{End}^0(J)$	$\GL_2\textsf{-type}$	Sato-Tate	Nonmaximal primes	$\Q$-simple	\(\overline{\Q}\)-simple	\(\Aut(X)\)	\(\Aut(X_{\overline{\Q}})\)	$\Q$-points	$\Q$-Weierstrass points	mod-$\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
17689.e.866761.1	17689.e	\( 7^{2} \cdot 19^{2} \)	\( 7^{4} \cdot 19^{2} \)	$0$	$2$	$\Z/5\Z$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$0$	$0$	2.12.2, 3.72.2	✓	✓	$4$	\( 5 \)	\(1.000000\)	\(2.783152\)	\(2.226521\)	$[82660,1,-22227071,110945408]$	$[20665,17793426,20428150568,26385430667561,866761]$	$[\frac{3768574004844424665625}{866761},\frac{22431988071545220750}{123823},\frac{178034344310076200}{17689}]$	$y^2 + (x^3 + x + 1)y = -x^6 - x^5 + 7x^4 + 7x^3 - 28x^2 - 13x + 34$

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