Genus 2 Curve Search Results

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

Results (displaying matches 1-50 of 63310)

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
249.a.249.1	249.a	\(y^2 + (x^3 + 1)y = x^2 + x\)	$\mathrm{USp}(4)$	✓		0
249.a.6723.1	249.a	\(y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2\)	$\mathrm{USp}(4)$	✓		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
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
363.a.11979.1	363.a	\(y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x\)	$G_{3,3}$		✓	0
363.a.43923.1	363.a	\(y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2\)	$G_{3,3}$		✓	0
388.a.776.1	388.a	\(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\)	$\mathrm{USp}(4)$	✓		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
394.a.3152.1	394.a	\(y^2 + (x + 1)y = -x^5\)	$\mathrm{USp}(4)$	✓		0
427.a.2989.1	427.a	\(y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4\)	$\mathrm{USp}(4)$	✓		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
464.a.29696.1	464.a	\(y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2\)	$\mathrm{USp}(4)$	✓		0
464.a.29696.2	464.a	\(y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x\)	$\mathrm{USp}(4)$	✓		0
472.a.944.1	472.a	\(y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x\)	$\mathrm{USp}(4)$	✓		0
472.a.60416.1	472.a	\(y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2\)	$\mathrm{USp}(4)$	✓		0
523.a.523.1	523.a	\(y^2 + (x + 1)y = x^5 - x^4 - x^3\)	$\mathrm{USp}(4)$	✓		0
523.a.523.2	523.a	\(y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x\)	$\mathrm{USp}(4)$	✓		0
529.a.529.1	529.a	\(y^2 + (x^3 + x + 1)y = -x^5\)	$G_{3,3}$	✓	✓	0
555.a.8325.1	555.a	\(y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x\)	$\mathrm{USp}(4)$	✓		0
574.a.293888.1	574.a	\(y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1\)	$\mathrm{USp}(4)$	✓		0
587.a.587.1	587.a	\(y^2 + (x^3 + x + 1)y = -x^2 - x\)	$\mathrm{USp}(4)$	✓		1
597.a.597.1	597.a	\(y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x\)	$\mathrm{USp}(4)$	✓		0
600.a.18000.1	600.a	\(y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x\)	$G_{3,3}$		✓	0
600.a.96000.1	600.a	\(y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2\)	$G_{3,3}$		✓	0
603.a.603.1	603.a	\(y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x\)	$\mathrm{USp}(4)$	✓		0
603.a.603.2	603.a	\(y^2 + (x^2 + 1)y = x^5 - x^3 + x\)	$\mathrm{USp}(4)$	✓		0
604.a.9664.1	604.a	\(y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21\)	$\mathrm{USp}(4)$	✓		0
604.a.9664.2	604.a	\(y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x\)	$\mathrm{USp}(4)$	✓		0
644.b.14812.1	644.b	\(y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1\)	$\mathrm{USp}(4)$	✓		0
688.a.2752.1	688.a	\(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\)	$\mathrm{USp}(4)$	✓		0
688.a.704512.2	688.a	\(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\)	$\mathrm{USp}(4)$	✓		0
688.a.704512.1	688.a	\(y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1\)	$\mathrm{USp}(4)$	✓		0
691.a.691.1	691.a	\(y^2 + (x + 1)y = x^5 - x^3 - x^2\)	$\mathrm{USp}(4)$	✓		0
704.a.45056.1	704.a	\(y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2\)	$\mathrm{USp}(4)$	✓		0
708.a.2832.1	708.a	\(y^2 + (x^2 + x + 1)y = x^5\)	$\mathrm{USp}(4)$	✓		0
708.a.19116.1	708.a	\(y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1\)	$\mathrm{USp}(4)$	✓		0
708.a.181248.1	708.a	\(y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36\)	$\mathrm{USp}(4)$	✓		0
709.a.709.1	709.a	\(y^2 + xy = x^5 - 2x^2 + x\)	$\mathrm{USp}(4)$	✓		0
713.a.713.1	713.a	\(y^2 + (x^3 + x + 1)y = -x^5 - x\)	$\mathrm{USp}(4)$	✓		1
713.b.713.1	713.b	\(y^2 + (x^3 + x + 1)y = -x^4\)	$\mathrm{USp}(4)$	✓		0
726.a.1452.1	726.a	\(y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x\)	$G_{3,3}$		✓	0
731.a.12427.1	731.a	\(y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3\)	$\mathrm{USp}(4)$	✓		0