Genus 2 curves in isogeny class 2646.b of discriminant 71442

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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
2646.b.71442.1	2646.b	\( 2 \cdot 3^{3} \cdot 7^{2} \)	\( 2 \cdot 3^{6} \cdot 7^{2} \)	$0$	$1$	$\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.90.3, 3.720.5	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(5.523621\)	\(0.690453\)	$[236,505,18451,37632]$	$[177,1116,15228,362475,71442]$	$[\frac{714924299}{294},\frac{12733498}{147},\frac{327214}{49}]$	$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + 3x - 1$

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