Genus 2 curves in isogeny class 1920.a of discriminant 368640

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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
1920.a.368640.1	1920.a	\( 2^{7} \cdot 3 \cdot 5 \)	\( - 2^{13} \cdot 3^{2} \cdot 5 \)	$0$	$3$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.6, 3.90.1			$2$	\( 2^{2} \)	\(1.000000\)	\(5.004698\)	\(0.625587\)	$[8952,6072,17987052,1440]$	$[17904,13340192,13237770240,14762078945024,368640]$	$[\frac{24952719973569408}{5},\frac{1038436236963696}{5},11510985848256]$	$y^2 + (x^3 + x^2 + x + 1)y = 5x^6 + 6x^5 + 17x^4 + 12x^3 + 17x^2 + 6x + 5$

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