Genus 2 curves of conductor 2080

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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
2080.a.4160.1	2080.a	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{6} \cdot 5 \cdot 13 \)	$1$	$2$	$\Z/4\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.1, 3.270.2	✓	✓	$1$	\( 2 \)	\(0.375514\)	\(7.057076\)	\(0.331254\)	$[49728,2307,38240328,520]$	$[49728,103034878,284642525440,884629355151359,4160]$	$[\frac{4751437160558113062912}{65},\frac{197973593207882440704}{65},169203148053037056]$	$y^2 + xy = x^6 + 12x^4 + 48x^2 + 65$
2080.a.4160.2	2080.a	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5 \cdot 13 \)	$1$	$2$	$\Z/4\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.270.2	✓	✓	$1$	\( 2 \)	\(0.375514\)	\(7.057076\)	\(0.331254\)	$[49728,2307,38240328,520]$	$[49728,103034878,284642525440,884629355151359,4160]$	$[\frac{4751437160558113062912}{65},\frac{197973593207882440704}{65},169203148053037056]$	$y^2 + xy = x^6 - 12x^4 + 48x^2 - 65$

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