Genus 2 curves of conductor 1376

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
1376.a.2752.1	1376.a	\( 2^{5} \cdot 43 \)	\( - 2^{6} \cdot 43 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(14.493471\)	\(0.452921\)	$[192,-528,-2760,-344]$	$[192,1888,64,-888064,-2752]$	$[-4076863488/43,-208797696/43,-36864/43]$	$y^2 + y = 2x^5 + 3x^4 - 2x^2$
1376.b.176128.1	1376.b	\( 2^{5} \cdot 43 \)	\( 2^{12} \cdot 43 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(8.781442\)	\(0.487858\)	$[122,2512,59936,-688]$	$[244,-4218,61436,-700285,-176128]$	$[-844596301/172,478702929/1376,-57150839/2752]$	$y^2 + y = 4x^5 + 4x^4 + x^3 + 2x^2$