Genus 2 curve search results

Results (17 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
169.a.169.1	169.a	$13^{2}$	$- 13^{2}$	$0$	$0$	$\Z/19\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_6$		✓		$C_6$	$D_6$	$6$	$0$	2.40.3, 3.480.12	✓	✓	$1$	$1$	$1.000000$	$32.667031$	$0.090490$	$[4,793,3757,-21632]$	$[1,-33,-43,-283,-169]$	$[-1/169,33/169,43/169]$	$y^2 + (x^3 + x + 1)y = x^5 + x^4$
249.a.249.1	249.a	$3 \cdot 83$	$3 \cdot 83$	$0$	$1$	$\Z/14\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$25.783703$	$0.131550$	$[108,57,2259,-31872]$	$[27,28,32,20,-249]$	$[-4782969/83,-183708/83,-7776/83]$	$y^2 + (x^3 + 1)y = x^2 + x$
277.a.277.1	277.a	$277$	$277$	$0$	$0$	$\Z/15\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3,5$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1, 3.80.1	✓	✓	$1$	$1$	$1.000000$	$32.205749$	$0.143137$	$[64,352,9552,-1108]$	$[32,-16,-464,-3776,-277]$	$[-33554432/277,524288/277,475136/277]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$
277.a.277.2	277.a	$277$	$277$	$0$	$0$	$\Z/5\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3,5$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1, 3.80.2	✓	✓	$1$	$1$	$1.000000$	$3.578417$	$0.143137$	$[4480,1370512,1511819744,-1108]$	$[2240,-19352,164384,-1569936,-277]$	$[-56394933862400000/277,217505333248000/277,-824813158400/277]$	$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$
294.a.294.1	294.a	$2 \cdot 3 \cdot 7^{2}$	$- 2 \cdot 3 \cdot 7^{2}$	$0$	$1$	$\Z/12\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.45.1, 3.720.4	✓	✓	$1$	$1$	$1.000000$	$21.451533$	$0.148969$	$[236,505,18451,37632]$	$[59,124,564,4475,294]$	$[714924299/294,12733498/147,327214/49]$	$y^2 + (x^3 + 1)y = x^4 + x^2$
295.a.295.1	295.a	$5 \cdot 59$	$- 5 \cdot 59$	$0$	$1$	$\Z/14\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$29.256600$	$0.149268$	$[108,-39,20835,37760]$	$[27,32,-256,-1984,295]$	$[14348907/295,629856/295,-186624/295]$	$y^2 + (x^3 + 1)y = -x^2$
295.a.295.2	295.a	$5 \cdot 59$	$- 5 \cdot 59$	$0$	$1$	$\Z/2\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$0.597073$	$0.149268$	$[198804,305807001,18482629056189,-37760]$	$[49701,90182600,203402032096,494095763610824,-295]$	$[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$	$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$
349.a.349.1	349.a	$349$	$349$	$0$	$0$	$\Z/13\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,13$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	$1$	$1.000000$	$27.988484$	$0.165612$	$[8,208,1464,-1396]$	$[4,-34,-124,-413,-349]$	$[-1024/349,2176/349,1984/349]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$
353.a.353.1	353.a	$353$	$-353$	$0$	$0$	$\Z/11\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,11$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.10.1	✓	✓	$1$	$1$	$1.000000$	$22.495495$	$0.185913$	$[188,817,30871,45184]$	$[47,58,256,2167,353]$	$[229345007/353,6021734/353,565504/353]$	$y^2 + (x^3 + x + 1)y = x^2$
389.a.389.1	389.a	$389$	$389$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$19.798620$	$0.197986$	$[2440,51100,45041351,1556]$	$[1220,53500,2084961,-79649395,389]$	$[2702708163200000/389,97147868000000/389,3103255952400/389]$	$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$
389.a.389.2	389.a	$389$	$389$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$19.798620$	$0.197986$	$[16,100,1775,1556]$	$[8,-14,-159,-367,389]$	$[32768/389,-7168/389,-10176/389]$	$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
394.a.394.1	394.a	$2 \cdot 197$	$2 \cdot 197$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$20.078274$	$0.200783$	$[11032,106300,393913607,1576]$	$[5516,1250044,371875905,122164372511,394]$	$[12960598758485504,532478222573696,28717744887720]$	$y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9$
448.a.448.2	448.a	$2^{6} \cdot 7$	$- 2^{6} \cdot 7$	$0$	$1$	$\Z/12\Z$	$\mathsf{CM} \times \Q$	$\Q \times \Q$	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.2160.5	✓	✓	$1$	$1$	$1.000000$	$31.171156$	$0.216466$	$[828,16635,5308452,56]$	$[828,17476,-853888,-253107460,448]$	$[6080953884912/7,155007628668/7,-1306723104]$	$y^2 + (x^3 + x)y = -2x^4 + 7$
448.a.448.1	448.a	$2^{6} \cdot 7$	$2^{6} \cdot 7$	$0$	$1$	$\Z/6\Z$	$\mathsf{CM} \times \Q$	$\Q \times \Q$	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.45.1, 3.2160.5	✓	✓	$1$	$1$	$1.000000$	$7.792789$	$0.216466$	$[828,16635,5308452,56]$	$[828,17476,-853888,-253107460,448]$	$[6080953884912/7,155007628668/7,-1306723104]$	$y^2 + (x^3 + x)y = x^4 - 7$
461.a.461.1	461.a	$461$	$461$	$0$	$0$	$\Z/7\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	$1$	$1.000000$	$12.048435$	$0.245886$	$[1176,144,66456,1844]$	$[588,14382,467132,16957923,461]$	$[70288881159168/461,2923824242304/461,161508086208/461]$	$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$
461.a.461.2	461.a	$461$	$461$	$0$	$0$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	$1$	$1.000000$	$0.245886$	$0.245886$	$[80664,166117104,3752725952952,1844]$	$[40332,40091742,45075737276,52661714805267,461]$	$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$	$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$
464.a.464.1	464.a	$2^{4} \cdot 29$	$2^{4} \cdot 29$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$14.421431$	$0.225335$	$[136,280,15060,1856]$	$[68,146,-64,-6417,464]$	$[90870848/29,2869192/29,-18496/29]$	$y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$

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