Genus 2 curves of conductor 768

Results (displaying both matches)

 

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
768.a.1536.1	768.a	\( 2^{8} \cdot 3 \)	\( 2^{9} \cdot 3 \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.180.3, 3.80.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(25.146749\)	\(0.349260\)	$[134,82,3600,6]$	$[268,2774,35236,437043,1536]$	$[2700250214/3,417158281/12,39543601/24]$	$y^2 + y = 2x^5 - x^4 - 3x^3 + x$
768.a.4608.1	768.a	\( 2^{8} \cdot 3 \)	\( 2^{9} \cdot 3^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.180.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(12.573375\)	\(0.349260\)	$[38,22,384,18]$	$[76,182,-476,-17325,4608]$	$[4952198/9,624169/36,-42959/72]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1$