Genus 2 Curve Search Results

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Conductor	Discriminant	Rational points*	Weierstrass	Torsion order	Torsion
2-Selmer rank	Analytic rank*	Analytic Ш*	Square Ш*	\(\GL_2\)-type	\(\mathrm{ST}\)
\(\mathrm{ST}^0\)	\(\mathrm{Aut}(X)\)	\(\mathrm{Aut}(X_{\overline{\Q}})\)	\(\overline{\Q}\)-end algebra	Locally solvable	\(\overline{\mathbb Q}\)-simple
Bad primes

Results (displaying all 17 matches)

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
169.a.169.1	169.a	\(y^2 + (x^3 + x + 1)y = x^5 + x^4\)	$E_6$		✓	0
249.a.249.1	249.a	\(y^2 + (x^3 + 1)y = x^2 + x\)	$\mathrm{USp}(4)$	✓		0
277.a.277.1	277.a	\(y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x\)	$\mathrm{USp}(4)$	✓		0
277.a.277.2	277.a	\(y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6\)	$\mathrm{USp}(4)$	✓		0
294.a.294.1	294.a	\(y^2 + (x^3 + 1)y = x^4 + x^2\)	$G_{3,3}$		✓	0
295.a.295.1	295.a	\(y^2 + (x^3 + 1)y = -x^2\)	$\mathrm{USp}(4)$	✓		0
295.a.295.2	295.a	\(y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608\)	$\mathrm{USp}(4)$	✓		0
349.a.349.1	349.a	\(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2\)	$\mathrm{USp}(4)$	✓		0
353.a.353.1	353.a	\(y^2 + (x^3 + x + 1)y = x^2\)	$\mathrm{USp}(4)$	✓		0
389.a.389.1	389.a	\(y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7\)	$\mathrm{USp}(4)$	✓		0
389.a.389.2	389.a	\(y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\)	$\mathrm{USp}(4)$	✓		0
394.a.394.1	394.a	\(y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9\)	$\mathrm{USp}(4)$	✓		0
448.a.448.2	448.a	\(y^2 + (x^3 + x)y = -2x^4 + 7\)	$N(G_{1,3})$		✓	0
448.a.448.1	448.a	\(y^2 + (x^3 + x)y = x^4 - 7\)	$N(G_{1,3})$		✓	0
461.a.461.1	461.a	\(y^2 + x^3y = x^5 - 3x^3 + 3x - 2\)	$\mathrm{USp}(4)$	✓		0
461.a.461.2	461.a	\(y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306\)	$\mathrm{USp}(4)$	✓		0
464.a.464.1	464.a	\(y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3\)	$\mathrm{USp}(4)$	✓		0