Genus 2 curves of conductor 1145

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
1145.a.1145.1	1145.a	\( 5 \cdot 229 \)	\( 5 \cdot 229 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.60.1	✓	✓	$1$	\( 1 \)	\(0.026504\)	\(29.585150\)	\(0.196028\)	$[468,5337,771165,146560]$	$[117,348,224,-23724,1145]$	$[21924480357/1145,557361324/1145,3066336/1145]$	$y^2 + (x^3 + 1)y = -3x^4 + 3x^3 - x$
1145.a.143125.1	1145.a	\( 5 \cdot 229 \)	\( - 5^{4} \cdot 229 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.15.1	✓	✓	$1$	\( 2^{2} \)	\(0.026504\)	\(7.396287\)	\(0.196028\)	$[5004,191097,289856403,18320000]$	$[1251,57246,3273124,204393402,143125]$	$[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$	$y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$