Genus 2 curves of conductor 603

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
603.a.603.1	603.a	\( 3^{2} \cdot 67 \)	\( - 3^{2} \cdot 67 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(26.910016\)	\(0.269100\)	$[1672,75628,49887881,2412]$	$[836,16516,-1263521,-332270453,603]$	$[408348897330176/603,9649919856896/603,-883069772816/603]$	$y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2	603.a	\( 3^{2} \cdot 67 \)	\( - 3^{2} \cdot 67 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(26.910016\)	\(0.269100\)	$[176,148,7375,-2412]$	$[88,298,1361,7741,-603]$	$[-5277319168/603,-203078656/603,-10539584/603]$	$y^2 + (x^2 + 1)y = x^5 - x^3 + x$