Genus 2 curves in isogeny class 12544.g of discriminant 175616

Results (unique match)

 

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
12544.g.175616.1	12544.g	\( 2^{8} \cdot 7^{2} \)	\( - 2^{9} \cdot 7^{3} \)	$1$	$2$	$\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_4)$		✓		$C_2$	$D_4$	$6$	$0$	2.90.1, 3.270.1	✓	✓	$1$	\( 2 \cdot 3 \)	\(0.046418\)	\(11.290429\)	\(0.786126\)	$[8,-203,455,686]$	$[16,552,-5632,-98704,175616]$	$[2048/343,4416/343,-2816/343]$	$y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$