Genus 2 curve search results

Results (3 matches)

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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
1180.a.18880.1	1180.a	\( 2^{2} \cdot 5 \cdot 59 \)	\( - 2^{6} \cdot 5 \cdot 59 \)	$0$	$1$	$\Z/18\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(24.170512\)	\(0.447602\)	$[916,23257,5960477,-2416640]$	$[229,1216,6656,11392,-18880]$	$[-\frac{629763392149}{18880},-\frac{228170791}{295},-\frac{5453864}{295}]$	$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$
1728.a.27648.1	1728.a	\( 2^{6} \cdot 3^{3} \)	\( - 2^{10} \cdot 3^{3} \)	$0$	$1$	$\Z/18\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 3^{2} \)	\(1.000000\)	\(22.164198\)	\(0.615672\)	$[324,2259,289890,3456]$	$[324,2868,-43408,-5572404,27648]$	$[129140163,\frac{14112711}{4},-\frac{659259}{4}]$	$y^2 + (x + 1)y = 3x^6 - 3x^4 - x^3$
2320.b.185600.1	2320.b	\( 2^{4} \cdot 5 \cdot 29 \)	\( 2^{8} \cdot 5^{2} \cdot 29 \)	$0$	$1$	$\Z/18\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 2 \cdot 3^{2} \)	\(1.000000\)	\(13.382897\)	\(0.743494\)	$[208,2248,126644,-742400]$	$[104,76,-644,-18188,-185600]$	$[-\frac{47525504}{725},-\frac{333944}{725},\frac{27209}{725}]$	$y^2 + (x^3 + x)y = -x^4 - x^3 - x + 1$

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