Genus 2 curve search results

Results (50 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
256.a.512.1	256.a	$2^{8}$	$- 2^{9}$	$0$	$2$	$\Z/2\Z\oplus\Z/10\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$6$	$2$	2.180.3, 3.540.6	✓	✓	$1$	$2$	$1.000000$	$26.841829$	$0.134209$	$[26,-2,40,2]$	$[52,118,-36,-3949,512]$	$[742586,129623/4,-1521/8]$	$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
400.a.409600.1	400.a	$2^{4} \cdot 5^{2}$	$- 2^{14} \cdot 5^{2}$	$0$	$1$	$\Z/3\Z\oplus\Z/6\Z$	$\mathrm{M}_2(\Q)$	$\mathrm{M}_2(\Q)$		$E_1$				$D_4$	$D_4$	$4$	$0$	2.180.4, 3.17280.4	✓	✓	$1$	$3^{2}$	$1.000000$	$7.977095$	$0.221586$	$[248,181,14873,50]$	$[992,39072,1945600,100853504,409600]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 = x^6 + 4x^4 + 4x^2 + 1$
576.a.576.1	576.a	$2^{6} \cdot 3^{2}$	$- 2^{6} \cdot 3^{2}$	$0$	$1$	$\Z/10\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_2$		✓		$C_4$	$D_4$	$4$	$0$	2.180.4, 3.1080.16	✓	✓	$1$	$1$	$1.000000$	$22.396252$	$0.223963$	$[68,124,2616,72]$	$[68,110,-36,-3637,576]$	$[22717712/9,540430/9,-289]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1	576.b	$2^{6} \cdot 3^{2}$	$- 2^{14} \cdot 3^{2}$	$0$	$2$	$\Z/4\Z\oplus\Z/4\Z$	$\mathrm{M}_2(\Q)$	$\mathrm{M}_2(\Q)$		$E_1$				$D_4$	$D_4$	$4$	$0$	2.180.7, 3.2160.25	✓	✓	$1$	$2^{3}$	$1.000000$	$9.301119$	$0.290660$	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = x^6 + 2x^4 + 2x^2 + 1$
1152.a.147456.1	1152.a	$2^{7} \cdot 3^{2}$	$2^{14} \cdot 3^{2}$	$0$	$1$	$\Z/8\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	$2^{2}$	$1.000000$	$7.270694$	$0.454418$	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = x^6 - 2x^4 + 2x^2 - 1$
1600.b.409600.1	1600.b	$2^{6} \cdot 5^{2}$	$2^{14} \cdot 5^{2}$	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.360.1, 3.8640.8	✓	✓	$1$	$2 \cdot 3$	$1.000000$	$12.846191$	$0.535258$	$[248,181,14873,50]$	$[992,39072,1945600,100853504,409600]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 = x^6 - 4x^4 + 4x^2 - 1$
2304.b.147456.1	2304.b	$2^{8} \cdot 3^{2}$	$- 2^{14} \cdot 3^{2}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathrm{M}_2(\Q)$		$E_1$				$D_4$	$D_4$	$0$	$0$	2.180.7, 3.2160.25		✓	$1$	$2$	$1.000000$	$5.683509$	$0.710439$	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = -x^6 - 2x^4 - 2x^2 - 1$
4096.e.524288.1	4096.e	$2^{12}$	$- 2^{19}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$2$	$2$	2.180.3, 3.540.6	✓	✓	$1$	$2$	$1.000000$	$7.402544$	$0.925318$	$[26,-2,40,2]$	$[208,1888,-2304,-1010944,524288]$	$[742586,129623/4,-1521/8]$	$y^2 = x^5 - 2x^4 - 2x^2 - x$
4608.a.4608.1	4608.a	$2^{9} \cdot 3^{2}$	$- 2^{9} \cdot 3^{2}$	$0$	$1$	$\Z/4\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$0$	2.90.5, 3.1080.10	✓	✓	$1$	$1$	$1.000000$	$13.153769$	$0.822111$	$[152,109,5469,18]$	$[304,3560,50688,683888,4608]$	$[5071050752/9,195344320/9,1016576]$	$y^2 + x^3y = x^4 + 2x^2 + 2$
4608.b.4608.1	4608.b	$2^{9} \cdot 3^{2}$	$2^{9} \cdot 3^{2}$	$0$	$1$	$\Z/4\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$0$	2.90.5, 3.1080.10	✓	✓	$1$	$1$	$1.000000$	$10.282314$	$0.642645$	$[152,109,5469,18]$	$[304,3560,50688,683888,4608]$	$[5071050752/9,195344320/9,1016576]$	$y^2 + x^3y = -x^4 + 2x^2 - 2$
4608.c.27648.1	4608.c	$2^{9} \cdot 3^{2}$	$- 2^{10} \cdot 3^{3}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.540.5	✓	✓	$1$	$2^{2}$	$1.000000$	$13.756159$	$0.859760$	$[24,-72,-180,108]$	$[48,288,-1024,-33024,27648]$	$[9216,1152,-256/3]$	$y^2 = x^5 - x^4 + x^2 - x$
6400.b.12800.1	6400.b	$2^{8} \cdot 5^{2}$	$- 2^{9} \cdot 5^{2}$	$0$	$1$	$\Z/6\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$0$	2.180.4, 3.8640.8	✓	✓	$1$	$3$	$1.000000$	$11.281316$	$0.940110$	$[248,181,14873,50]$	$[496,9768,243200,6303344,12800]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 + x^3y = 2x^4 + 4x^2 + 2$
6400.d.12800.1	6400.d	$2^{8} \cdot 5^{2}$	$2^{9} \cdot 5^{2}$	$1$	$2$	$\Z/6\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$6$	$0$	2.180.4, 3.8640.8	✓	✓	$1$	$3$	$0.413437$	$18.167258$	$0.625918$	$[248,181,14873,50]$	$[496,9768,243200,6303344,12800]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 + x^3y = -2x^4 + 4x^2 - 2$
6400.f.64000.1	6400.f	$2^{8} \cdot 5^{2}$	$- 2^{9} \cdot 5^{3}$	$2$	$4$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$16$	$0$	2.90.6, 3.540.6	✓	✓	$1$	$2^{2}$	$0.067032$	$19.455210$	$0.326031$	$[154,310,19480,250]$	$[308,3126,-164,-2455597,64000]$	$[5413568314/125,713561079/500,-243089/1000]$	$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$
6400.g.64000.1	6400.g	$2^{8} \cdot 5^{2}$	$- 2^{9} \cdot 5^{3}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$2$	$2$	2.180.3, 3.540.6	✓	✓	$1$	$2^{2}$	$1.000000$	$6.303153$	$1.575788$	$[154,310,19480,250]$	$[308,3126,-164,-2455597,64000]$	$[5413568314/125,713561079/500,-243089/1000]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$
6400.i.409600.1	6400.i	$2^{8} \cdot 5^{2}$	$- 2^{14} \cdot 5^{2}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathrm{M}_2(\Q)$		$E_1$				$D_4$	$D_4$	$0$	$0$	2.180.4, 3.8640.12		✓	$1$	$1$	$1.000000$	$5.171827$	$1.292957$	$[248,181,14873,50]$	$[992,39072,1945600,100853504,409600]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 = -x^6 - 4x^4 - 4x^2 - 1$
8192.a.32768.1	8192.a	$2^{13}$	$2^{15}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.270.1	✓	✓	$1$	$2^{2}$	$1.000000$	$16.855414$	$1.053463$	$[67,82,1930,4]$	$[268,2118,-124,-1129789,32768]$	$[1350125107/32,318508017/256,-139159/512]$	$y^2 = x^5 - 3x^3 + 2x$
8192.b.131072.1	8192.b	$2^{13}$	$2^{17}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_2)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.540.3	✓	✓	$1$	$2^{2}$	$1.000000$	$15.683046$	$0.980190$	$[64,76,1552,16]$	$[256,1920,8192,-397312,131072]$	$[8388608,245760,4096]$	$y^2 = x^5 - 3x^4 + 6x^2 - 4x$
9216.a.36864.1	9216.a	$2^{10} \cdot 3^{2}$	$2^{12} \cdot 3^{2}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.360.1, 3.1080.10	✓	✓	$1$	$2$	$1.000000$	$9.381457$	$1.172682$	$[46,-44,-72,144]$	$[92,470,-684,-70957,36864]$	$[6436343/36,2859245/288,-10051/64]$	$y^2 = x^5 + x^3 + x$
12544.d.25088.1	12544.d	$2^{8} \cdot 7^{2}$	$- 2^{9} \cdot 7^{2}$	$2$	$3$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$12$	$0$	2.45.1, 3.540.6	✓	✓	$1$	$2$	$0.058077$	$15.061274$	$0.437354$	$[74,142,3272,98]$	$[148,534,-196,-78541,25088]$	$[138687914/49,13524351/196,-1369/8]$	$y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$
12544.g.175616.1	12544.g	$2^{8} \cdot 7^{2}$	$- 2^{9} \cdot 7^{3}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$6$	$0$	2.90.1, 3.270.1	✓	✓	$1$	$2 \cdot 3$	$0.046418$	$11.290429$	$0.786126$	$[8,-203,455,686]$	$[16,552,-5632,-98704,175616]$	$[2048/343,4416/343,-2816/343]$	$y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$
12800.c.128000.1	12800.c	$2^{9} \cdot 5^{2}$	$2^{10} \cdot 5^{3}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.270.1	✓	✓	$1$	$2^{2}$	$1.000000$	$15.952863$	$0.997054$	$[104,280,9140,500]$	$[208,1056,-1024,-332032,128000]$	$[380204032/125,9280128/125,-43264/125]$	$y^2 = x^5 - 3x^4 + 3x^2 - x$
16384.a.32768.1	16384.a	$2^{14}$	$2^{15}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.180.3, 3.270.1	✓	✓	$1$	$2$	$1.000000$	$8.427707$	$1.053463$	$[67,82,1930,4]$	$[268,2118,-124,-1129789,32768]$	$[1350125107/32,318508017/256,-139159/512]$	$y^2 = x^5 + 3x^3 + 2x$
25600.a.102400.1	25600.a	$2^{10} \cdot 5^{2}$	$2^{12} \cdot 5^{2}$	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.360.1, 3.1080.10	✓	✓	$1$	$2$	$0.717386$	$16.418098$	$1.472264$	$[94,244,7096,400]$	$[188,822,-1100,-220621,102400]$	$[229345007/100,42671253/800,-24299/64]$	$y^2 = x^5 - 3x^3 + x$
25600.d.128000.1	25600.d	$2^{10} \cdot 5^{2}$	$- 2^{10} \cdot 5^{3}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$2$	$2$	2.180.3, 3.540.6	✓	✓	$1$	$2$	$1.000000$	$13.879043$	$1.734880$	$[56,-80,-260,500]$	$[112,736,-1536,-178432,128000]$	$[17210368/125,1009792/125,-18816/125]$	$y^2 = x^5 + x^4 + x^2 - x$
25600.e.128000.1	25600.e	$2^{10} \cdot 5^{2}$	$- 2^{10} \cdot 5^{3}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$2$	$2$	2.180.3, 3.540.6	✓	✓	$1$	$2$	$1.000000$	$9.947770$	$1.243471$	$[56,-80,-260,500]$	$[112,736,-1536,-178432,128000]$	$[17210368/125,1009792/125,-18816/125]$	$y^2 = x^5 - x^4 - x^2 - x$
36864.b.36864.1	36864.b	$2^{12} \cdot 3^{2}$	$2^{12} \cdot 3^{2}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	$1$	$0.675802$	$9.381457$	$1.585002$	$[46,-44,-72,144]$	$[92,470,-684,-70957,36864]$	$[6436343/36,2859245/288,-10051/64]$	$y^2 = x^5 - x^3 + x$
69696.c.627264.1	69696.c	$2^{6} \cdot 3^{2} \cdot 11^{2}$	$- 2^{6} \cdot 3^{4} \cdot 11^{2}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_2$		✓		$C_4$	$D_4$	$0$	$0$	2.180.4, 3.1080.16		✓	$1$	$2$	$1.000000$	$7.488051$	$3.744026$	$[1220,3580,1448760,78408]$	$[1220,59630,3724380,247001675,627264]$	$[42229815050000/9801,1691859628750/9801,8837375]$	$y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$
73728.c.884736.1	73728.c	$2^{13} \cdot 3^{2}$	$2^{15} \cdot 3^{3}$	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.180.3, 3.270.1	✓	✓	$1$	$2^{3}$	$0.793842$	$5.583154$	$2.216071$	$[195,630,44910,108]$	$[780,18630,-380,-86843325,884736]$	$[10442615625/32,2558131875/256,-401375/1536]$	$y^2 = x^5 + 5x^3 + 6x$
73728.d.884736.1	73728.d	$2^{13} \cdot 3^{2}$	$2^{15} \cdot 3^{3}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.270.1	✓	✓	$1$	$2^{3}$	$1.000000$	$11.166308$	$1.395789$	$[195,630,44910,108]$	$[780,18630,-380,-86843325,884736]$	$[10442615625/32,2558131875/256,-401375/1536]$	$y^2 = 2x^5 - 5x^3 + 3x$
78400.a.78400.1	78400.a	$2^{6} \cdot 5^{2} \cdot 7^{2}$	$- 2^{6} \cdot 5^{2} \cdot 7^{2}$	$0$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_2$		✓		$C_4$	$D_4$	$0$	$0$	2.90.5, 3.1080.16			$2$	$1$	$1.000000$	$6.009550$	$3.004775$	$[452,1276,189752,9800]$	$[452,7662,151900,2488139,78400]$	$[294789628688/1225,11055476814/1225,395839]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$
102400.b.102400.1	102400.b	$2^{12} \cdot 5^{2}$	$- 2^{12} \cdot 5^{2}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_2)$		✓		$C_2$	$D_4$	$4$	$2$	2.90.3, 3.540.2	✓	✓	$1$	$1$	$0.797280$	$12.084061$	$2.408596$	$[34,-116,-424,400]$	$[68,502,-2100,-98701,102400]$	$[1419857/100,1233163/800,-6069/64]$	$y^2 = x^5 - x^3 - x$
102400.e.102400.1	102400.e	$2^{12} \cdot 5^{2}$	$2^{12} \cdot 5^{2}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	$1$	$1.000000$	$8.209049$	$2.052262$	$[94,244,7096,400]$	$[188,822,-1100,-220621,102400]$	$[229345007/100,42671253/800,-24299/64]$	$y^2 = x^5 + 3x^3 + x$
135424.l.270848.1	135424.l	$2^{8} \cdot 23^{2}$	$- 2^{9} \cdot 23^{2}$	$0$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$0$	$0$	2.45.1, 3.540.6			$2$	$2$	$1.000000$	$5.075262$	$5.075262$	$[170,430,23560,1058]$	$[340,3670,31740,-669325,270848]$	$[8874106250/529,1126919375/2116,108375/8]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 2x^4 - x^3 - 2x^2 - x - 1$
147456.c.884736.1	147456.c	$2^{14} \cdot 3^{2}$	$2^{15} \cdot 3^{3}$	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.180.3, 3.270.1	✓	✓	$1$	$2^{2}$	$1.000000$	$5.583154$	$1.395789$	$[195,630,44910,108]$	$[780,18630,-380,-86843325,884736]$	$[10442615625/32,2558131875/256,-401375/1536]$	$y^2 = 2x^5 + 5x^3 + 3x$
147456.e.884736.1	147456.e	$2^{14} \cdot 3^{2}$	$2^{15} \cdot 3^{3}$	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$2$	2.180.3, 3.270.1	✓	✓	$1$	$2^{2}$	$0.970167$	$11.166308$	$2.708295$	$[195,630,44910,108]$	$[780,18630,-380,-86843325,884736]$	$[10442615625/32,2558131875/256,-401375/1536]$	$y^2 = x^5 - 5x^3 + 6x$
193600.d.968000.1	193600.d	$2^{6} \cdot 5^{2} \cdot 11^{2}$	$- 2^{6} \cdot 5^{3} \cdot 11^{2}$	$0$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$0$	$0$	2.45.1, 3.540.6			$2$	$2$	$1.000000$	$3.888937$	$3.888937$	$[292,2380,214520,121000]$	$[292,1966,-4356,-1284277,968000]$	$[33169145488/15125,764807422/15125,-47961/125]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^4 - x^3 - x^2 - x - 1$
193600.e.968000.1	193600.e	$2^{6} \cdot 5^{2} \cdot 11^{2}$	$- 2^{6} \cdot 5^{3} \cdot 11^{2}$	$2$	$3$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_4$		✓		$C_4$	$D_4$	$8$	$0$	2.45.1, 3.540.6	✓	✓	$1$	$2$	$0.208207$	$11.078708$	$1.153332$	$[292,2380,214520,121000]$	$[292,1966,-4356,-1284277,968000]$	$[33169145488/15125,764807422/15125,-47961/125]$	$y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 + 2x^2 - x$
262144.a.262144.1	262144.a	$2^{18}$	$- 2^{18}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_2)$		✓		$C_2$	$D_4$	$2$	$2$	2.90.3, 3.3240.5	✓	✓	$1$	$1$	$1.123513$	$10.883805$	$3.057023$	$[4,-14,2,1]$	$[32,640,-6144,-151552,262144]$	$[128,80,-24]$	$y^2 = x^5 - 2x^3 - x$
262144.b.524288.1	262144.b	$2^{18}$	$2^{19}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.90.3, 3.270.1	✓	✓	$1$	$2$	$0.970077$	$7.048011$	$3.418555$	$[26,-2,40,2]$	$[208,1888,-2304,-1010944,524288]$	$[742586,129623/4,-1521/8]$	$y^2 = x^5 + 2x^3 + 2x$
262144.c.524288.1	262144.c	$2^{18}$	$2^{19}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$2$	2.90.3, 3.270.1	✓	✓	$1$	$2$	$0.759196$	$7.048011$	$2.675411$	$[26,-2,40,2]$	$[208,1888,-2304,-1010944,524288]$	$[742586,129623/4,-1521/8]$	$y^2 = x^5 - 2x^3 + 2x$
278784.a.557568.1	278784.a	$2^{8} \cdot 3^{2} \cdot 11^{2}$	$2^{9} \cdot 3^{2} \cdot 11^{2}$	$0$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$0$	$0$	2.90.5, 3.1080.10			$2$	$1$	$1.000000$	$5.710508$	$2.855254$	$[1592,1189,630369,2178]$	$[3184,419240,73041408,14200416368,557568]$	$[639139022845952/1089,26430898598080/1089,1328059136]$	$y^2 + y = 6x^6 - 8x^4 + 4x^2 - 1$
278784.b.557568.1	278784.b	$2^{8} \cdot 3^{2} \cdot 11^{2}$	$- 2^{9} \cdot 3^{2} \cdot 11^{2}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$0$	$0$	2.90.5, 3.1080.10		✓	$1$	$1$	$2.415493$	$4.989405$	$3.012968$	$[1592,1189,630369,2178]$	$[3184,419240,73041408,14200416368,557568]$	$[639139022845952/1089,26430898598080/1089,1328059136]$	$y^2 + y = -6x^6 - 8x^4 - 4x^2 - 1$
331776.e.995328.1	331776.e	$2^{12} \cdot 3^{4}$	$2^{12} \cdot 3^{5}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.90.3, 3.540.7	✓	✓	$1$	$2$	$1.000000$	$6.346552$	$3.173276$	$[58,28,856,16]$	$[348,4374,-1836,-4942701,995328]$	$[20511149/4,5926527/32,-14297/64]$	$y^2 = x^5 + 3x^3 + 3x$
331776.g.995328.1	331776.g	$2^{12} \cdot 3^{4}$	$2^{12} \cdot 3^{5}$	$1$	$2$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$2$	2.90.3, 3.540.7	✓	✓	$1$	$2$	$0.770890$	$6.346552$	$2.446248$	$[58,28,856,16]$	$[348,4374,-1836,-4942701,995328]$	$[20511149/4,5926527/32,-14297/64]$	$y^2 = x^5 - 3x^3 + 3x$
589824.a.589824.1	589824.a	$2^{16} \cdot 3^{2}$	$2^{16} \cdot 3^{2}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	$1$	$1.000000$	$13.759439$	$3.439860$	$[68,124,2616,72]$	$[272,1760,-2304,-931072,589824]$	$[22717712/9,540430/9,-289]$	$y^2 = x^5 - 4x^3 + x$
589824.b.589824.1	589824.b	$2^{16} \cdot 3^{2}$	$2^{16} \cdot 3^{2}$	$2$	$3$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$2$	$2$	2.180.5, 3.1080.10	✓	✓	$1$	$1$	$2.544094$	$6.879720$	$4.375664$	$[68,124,2616,72]$	$[272,1760,-2304,-931072,589824]$	$[22717712/9,540430/9,-289]$	$y^2 = x^5 + 4x^3 + x$
692224.a.692224.1	692224.a	$2^{12} \cdot 13^{2}$	$- 2^{12} \cdot 13^{2}$	$0$	$1$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q$		$J(E_2)$		✓		$C_2$	$D_4$	$2$	$2$	2.90.3, 3.540.2	✓	✓	$1$	$1$	$1.000000$	$9.748988$	$2.437247$	$[14,-404,-3928,-2704]$	$[28,1110,19604,-170797,-692224]$	$[-16807/676,-190365/5408,-1421/64]$	$y^2 = x^5 - 3x^3 - x$
778752.b.778752.1	778752.b	$2^{9} \cdot 3^{2} \cdot 13^{2}$	$2^{9} \cdot 3^{2} \cdot 13^{2}$	$2$	$3$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$0$	2.90.5, 3.1080.10	✓	✓	$1$	$1$	$1.538669$	$10.957992$	$4.215180$	$[1880,1405,879765,3042]$	$[3760,585320,120706560,27814290800,778752]$	$[1467808044800000/1521,60769678360000/1521,2191328000]$	$y^2 + y = 6x^6 - 10x^4 + 5x^2 - 1$
778752.c.778752.1	778752.c	$2^{9} \cdot 3^{2} \cdot 13^{2}$	$- 2^{9} \cdot 3^{2} \cdot 13^{2}$	$2$	$4$	$\Z/2\Z$	$\mathrm{M}_2(\Q)$	$\Q \times \Q$	✓	$J(E_1)$				$C_2^2$	$D_4$	$0$	$0$	2.90.5, 3.1080.10			$2$	$1$	$2.038974$	$4.813693$	$4.907496$	$[1880,1405,879765,3042]$	$[3760,585320,120706560,27814290800,778752]$	$[1467808044800000/1521,60769678360000/1521,2191328000]$	$y^2 + y = -6x^6 - 10x^4 - 5x^2 - 1$

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