Genus 2 curve search results

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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
504.a.27216.1	504.a	$2^{3} \cdot 3^{2} \cdot 7$	$- 2^{4} \cdot 3^{5} \cdot 7$	$0$	$2$	$\Z/4\Z\oplus\Z/4\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.6, 3.90.1	✓	✓	$1$	$2^{3}$	$1.000000$	$7.782699$	$0.243209$	$[8456,9496,26675348,108864]$	$[4228,743250,173847744,45651924783,27216]$	$[12063042849801664/243,167186257609000/81,3083035208512/27]$	$y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
523.a.523.1	523.a	$523$	$-523$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$24.819904$	$0.248199$	$[120,-540,-29169,-2092]$	$[60,240,2241,19215,-523]$	$[-777600000/523,-51840000/523,-8067600/523]$	$y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2	523.a	$523$	$-523$	$0$	$1$	$\Z/2\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$2$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$0.992796$	$0.248199$	$[332400,10084860,1107044456391,-2092]$	$[166200,1149254190,10581558955401,109467476288772525,-523]$	$[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$	$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1	529.a	$23^{2}$	$23^{2}$	$0$	$0$	$\Z/11\Z$	$\mathsf{RM}$	$\mathsf{RM}$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$4$	$0$	2.120.2, 3.432.4	✓	✓	$1$	$1$	$1.000000$	$30.060256$	$0.248432$	$[284,2401,246639,-67712]$	$[71,110,-624,-14101,-529]$	$[-1804229351/529,-39370210/529,3145584/529]$	$y^2 + (x^3 + x + 1)y = -x^5$
555.a.8325.1	555.a	$3 \cdot 5 \cdot 37$	$3^{2} \cdot 5^{2} \cdot 37$	$0$	$2$	$\Z/2\Z\oplus\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	$2^{2}$	$1.000000$	$25.692472$	$0.256925$	$[1264,18124,6869487,33300]$	$[632,13622,351361,9125317,8325]$	$[100828984082432/8325,3438682756096/8325,140342016064/8325]$	$y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
574.a.293888.1	574.a	$2 \cdot 7 \cdot 41$	$- 2^{10} \cdot 7 \cdot 41$	$0$	$2$	$\Z/2\Z\oplus\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.180.3	✓	✓	$1$	$2 \cdot 5$	$1.000000$	$11.546350$	$0.288659$	$[68,-55823,-955895,-37617664]$	$[17,2338,2304,-1356769,-293888]$	$[-1419857/293888,-820471/20992,-2601/1148]$	$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
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	✓	✓	$1$	$2^{3}$	$1.000000$	$9.301119$	$0.290660$	$[152,109,5469,18]$	$[608,14240,405504,10942208,147456]$	$[5071050752/9,195344320/9,1016576]$	$y^2 = x^6 + 2x^4 + 2x^2 + 1$
578.a.2312.1	578.a	$2 \cdot 17^{2}$	$2^{3} \cdot 17^{2}$	$0$	$1$	$\Z/12\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.2160.21	✓	✓	$1$	$3$	$1.000000$	$13.910299$	$0.289798$	$[228,705,135777,295936]$	$[57,106,-992,-16945,2312]$	$[601692057/2312,9815229/1156,-402876/289]$	$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
587.a.587.1	587.a	$587$	$587$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	$1$	$0.003773$	$29.510964$	$0.111352$	$[60,1401,54147,-75136]$	$[15,-49,-501,-2479,-587]$	$[-759375/587,165375/587,112725/587]$	$y^2 + (x^3 + x + 1)y = -x^2 - x$
588.a.18816.1	588.a	$2^{2} \cdot 3 \cdot 7^{2}$	$- 2^{7} \cdot 3 \cdot 7^{2}$	$0$	$1$	$\Z/24\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.45.1, 3.720.4	✓	✓	$1$	$2^{3}$	$1.000000$	$20.658150$	$0.286919$	$[748,11545,2902787,2408448]$	$[187,976,-192,-247120,18816]$	$[228669389707/18816,398891383/1176,-34969/98]$	$y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
597.a.597.1	597.a	$3 \cdot 199$	$3 \cdot 199$	$0$	$0$	$\Z/7\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	$1$	$1.000000$	$14.411617$	$0.294115$	$[120,192,9912,2388]$	$[60,118,-68,-4501,597]$	$[259200000/199,8496000/199,-81600/199]$	$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
600.a.18000.1	600.a	$2^{3} \cdot 3 \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{3}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$6$	$4$	2.360.2, 3.640.2	✓	✓	$1$	$2^{3}$	$1.000000$	$18.934319$	$0.262977$	$[1376,23824,11410044,72000]$	$[688,15752,244900,-19908576,18000]$	$[9634345320448/1125,320612931584/1125,289804864/45]$	$y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1	600.a	$2^{3} \cdot 3 \cdot 5^{2}$	$2^{8} \cdot 3 \cdot 5^{3}$	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$4$	$2$	2.180.3, 3.640.2	✓	✓	$1$	$2^{2}$	$1.000000$	$9.467159$	$0.262977$	$[92,4981,43947,-12000]$	$[92,-2968,47600,-1107456,-96000]$	$[-25745372/375,9027914/375,-62951/15]$	$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
600.b.30000.1	600.b	$2^{3} \cdot 3 \cdot 5^{2}$	$2^{4} \cdot 3 \cdot 5^{4}$	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$2$	2.180.3, 3.90.1	✓	✓	$1$	$2^{3}$	$1.000000$	$8.316291$	$0.259884$	$[600,18744,4690524,120000]$	$[300,626,-198336,-14973169,30000]$	$[81000000,563400,-595008]$	$y^2 + (x^3 + x)y = x^4 + x^2 - 3$
600.b.450000.1	600.b	$2^{3} \cdot 3 \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{5}$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$4$	2.360.2, 3.90.1	✓	✓	$1$	$2^{5}$	$1.000000$	$8.316291$	$0.259884$	$[18072,38904,233095932,1800000]$	$[9036,3395570,1698206400,953774351375,450000]$	$[418329622965299904/3125,3479436045234936/625,38515932506304/125]$	$y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
603.a.603.1	603.a	$3^{2} \cdot 67$	$- 3^{2} \cdot 67$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$26.910016$	$0.269100$	$[1672,75628,49887881,2412]$	$[836,16516,-1263521,-332270453,603]$	$[408348897330176/603,9649919856896/603,-883069772816/603]$	$y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2	603.a	$3^{2} \cdot 67$	$- 3^{2} \cdot 67$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$26.910016$	$0.269100$	$[176,148,7375,-2412]$	$[88,298,1361,7741,-603]$	$[-5277319168/603,-203078656/603,-10539584/603]$	$y^2 + (x^2 + 1)y = x^5 - x^3 + x$
604.a.9664.1	604.a	$2^{2} \cdot 151$	$2^{6} \cdot 151$	$0$	$0$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1, 3.720.5	✓	✓	$1$	$1$	$1.000000$	$0.291788$	$0.291788$	$[49556,-797087975,-23996873337603,1236992]$	$[12389,39607304,223396249616,299729401586052,9664]$	$[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$	$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2	604.a	$2^{2} \cdot 151$	$2^{6} \cdot 151$	$0$	$0$	$\Z/27\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1, 3.80.1	✓	✓	$1$	$3^{2}$	$1.000000$	$23.634831$	$0.291788$	$[116,6265,95277,1236992]$	$[29,-226,836,-6708,9664]$	$[20511149/9664,-2755957/4832,175769/2416]$	$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
630.a.34020.1	630.a	$2 \cdot 3^{2} \cdot 5 \cdot 7$	$2^{2} \cdot 3^{5} \cdot 5 \cdot 7$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$4$	2.360.2, 3.90.1	✓	✓	$1$	$2^{2}$	$1.000000$	$19.470889$	$0.304233$	$[24100,969793,7474503265,4354560]$	$[6025,1472118,470090880,166291536519,34020]$	$[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$	$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$
640.a.81920.1	640.a	$2^{7} \cdot 5$	$- 2^{14} \cdot 5$	$0$	$1$	$\Z/12\Z$	$\mathsf{CM} \times \Q$	$\Q \times \Q$	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.1, 3.2160.5	✓	✓	$1$	$2 \cdot 3$	$1.000000$	$7.405674$	$0.308570$	$[912,147,44562,10]$	$[3648,552928,111431680,25193348864,81920]$	$[39432490647552/5,1638374321664/5,18102076416]$	$y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2	640.a	$2^{7} \cdot 5$	$2^{14} \cdot 5$	$0$	$1$	$\Z/12\Z$	$\mathsf{CM} \times \Q$	$\Q \times \Q$	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$4$	$2$	2.90.3, 3.2160.5	✓	✓	$1$	$2 \cdot 3$	$1.000000$	$7.405674$	$0.308570$	$[912,147,44562,10]$	$[3648,552928,111431680,25193348864,81920]$	$[39432490647552/5,1638374321664/5,18102076416]$	$y^2 + x^3y = -3x^4 + 13x^2 - 20$
644.a.2576.1	644.a	$2^{2} \cdot 7 \cdot 23$	$- 2^{4} \cdot 7 \cdot 23$	$0$	$2$	$\Z/6\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.45.1, 3.720.4			$2$	$1$	$1.000000$	$3.928431$	$0.218246$	$[39036,4124865,50880984159,329728]$	$[9759,3796384,1910683600,1058457444236,2576]$	$[88516980336138032799/2576,220529201888022246/161,70640465629725]$	$y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$
644.a.659456.1	644.a	$2^{2} \cdot 7 \cdot 23$	$2^{12} \cdot 7 \cdot 23$	$0$	$1$	$\Z/2\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.90.3, 3.720.5	✓	✓	$1$	$1$	$1.000000$	$0.872985$	$0.218246$	$[161796,1070662305,46065265919409,84410368]$	$[40449,23560804,14638854160,9253881697856,659456]$	$[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$	$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
644.b.14812.1	644.b	$2^{2} \cdot 7 \cdot 23$	$- 2^{2} \cdot 7 \cdot 23^{2}$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.90.3	✓	✓	$1$	$2$	$1.000000$	$15.435107$	$0.308702$	$[1268,-40511,-17688719,-1895936]$	$[317,5875,170781,4905488,-14812]$	$[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$	$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
672.a.172032.1	672.a	$2^{5} \cdot 3 \cdot 7$	$2^{13} \cdot 3 \cdot 7$	$0$	$2$	$\Z/4\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.45.1, 3.720.5			$2$	$2$	$1.000000$	$1.113349$	$0.278337$	$[16916,151117825,232872423961,-21504]$	$[16916,-88822256,277597802496,-798387183476800,-172032]$	$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$	$y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$
676.a.5408.1	676.a	$2^{2} \cdot 13^{2}$	$- 2^{5} \cdot 13^{2}$	$0$	$0$	$\Z/21\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.60.2, 3.2160.21	✓	✓	$1$	$7$	$1.000000$	$20.169780$	$0.320155$	$[204,3273,161211,692224]$	$[51,-28,0,-196,5408]$	$[345025251/5408,-928557/1352,0]$	$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
676.a.562432.1	676.a	$2^{2} \cdot 13^{2}$	$2^{8} \cdot 13^{3}$	$0$	$0$	$\Z/21\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.60.2, 3.2160.20	✓	✓	$1$	$3 \cdot 7$	$1.000000$	$6.723260$	$0.320155$	$[1620,52953,29527389,71991296]$	$[405,4628,-8112,-6175936,562432]$	$[10896201253125/562432,5912281125/10816,-492075/208]$	$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
676.b.17576.1	676.b	$2^{2} \cdot 13^{2}$	$- 2^{3} \cdot 13^{3}$	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	$\mathrm{M}_2(\Q)$	$\mathrm{M}_2(\Q)$		$E_1$				$D_6$	$D_6$	$0$	$0$	2.120.4, 3.17280.1		✓	$1$	$3$	$1.000000$	$7.177121$	$0.265819$	$[1244,1249,129167,2249728]$	$[311,3978,72332,1667692,17576]$	$[2909390022551/17576,4602275343/676,10349147/26]$	$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
686.a.686.1	686.a	$2 \cdot 7^{3}$	$2 \cdot 7^{3}$	$0$	$1$	$\Z/6\Z$	$\mathsf{CM} \times \Q$	$\Q \times \Q$	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2^2$	$C_2^2$	$2$	$2$	2.90.3, 3.2160.5	✓	✓	$1$	$1$	$1.000000$	$11.491655$	$0.319213$	$[420,4305,640185,87808]$	$[105,280,-980,-45325,686]$	$[37209375/2,472500,-15750]$	$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
688.a.2752.1	688.a	$2^{4} \cdot 43$	$- 2^{6} \cdot 43$	$0$	$1$	$\Z/20\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.30.3	✓	✓	$1$	$5$	$1.000000$	$25.707298$	$0.321341$	$[32,112,-680,-344]$	$[32,-32,1344,10496,-2752]$	$[-524288/43,16384/43,-21504/43]$	$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
688.a.704512.2	688.a	$2^{4} \cdot 43$	$- 2^{14} \cdot 43$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$5$	$1.000000$	$6.426825$	$0.321341$	$[464,-248,-39602,-86]$	$[1856,146176,15688704,1937702912,-704512]$	$[-1344218660864/43,-57041383424/43,-3298550016/43]$	$y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1	688.a	$2^{4} \cdot 43$	$2^{14} \cdot 43$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	$5$	$1.000000$	$6.426825$	$0.321341$	$[128,532,26830,86]$	$[512,5248,-408576,-59183104,704512]$	$[2147483648/43,42991616/43,-6537216/43]$	$y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
691.a.691.1	691.a	$691$	$-691$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$18.812569$	$0.293946$	$[104,-824,-20333,-2764]$	$[52,250,601,-7812,-691]$	$[-380204032/691,-35152000/691,-1625104/691]$	$y^2 + (x + 1)y = x^5 - x^3 - x^2$
704.a.45056.1	704.a	$2^{6} \cdot 11$	$- 2^{12} \cdot 11$	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3, 3.80.1	✓	✓	$1$	$2^{2}$	$1.000000$	$11.976027$	$0.332667$	$[134,-464,-15328,-176]$	$[268,4230,61444,-356477,-45056]$	$[-1350125107/44,-636113745/352,-68955529/704]$	$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.2832.1	708.a	$2^{2} \cdot 3 \cdot 59$	$2^{4} \cdot 3 \cdot 59$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	$2$	$1.000000$	$16.267181$	$0.325344$	$[148,2065,76361,362496]$	$[37,-29,-59,-756,2832]$	$[69343957/2832,-1468937/2832,-1369/48]$	$y^2 + (x^2 + x + 1)y = x^5$
708.a.19116.1	708.a	$2^{2} \cdot 3 \cdot 59$	$- 2^{2} \cdot 3^{4} \cdot 59$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$2$	$1.000000$	$16.267181$	$0.325344$	$[908,-132815,8426215,2446848]$	$[227,7681,-438901,-39657072,19116]$	$[602738989907/19116,89845294523/19116,-383324231/324]$	$y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
708.a.181248.1	708.a	$2^{2} \cdot 3 \cdot 59$	$- 2^{10} \cdot 3 \cdot 59$	$0$	$3$	$\Z/2\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$0$	$0$	2.15.1	✓	✓	$4$	$1$	$1.000000$	$0.325344$	$0.325344$	$[234100,3468879025,202585466081177,-23199744]$	$[58525,-1820975,60952909,62829762150,-181248]$	$[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$	$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
709.a.709.1	709.a	$709$	$709$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$18.361162$	$0.286893$	$[160,-1280,-42089,2836]$	$[80,480,1121,-35180,709]$	$[3276800000/709,245760000/709,7174400/709]$	$y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1	713.a	$23 \cdot 31$	$23 \cdot 31$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$0$	2.20.2	✓	✓	$1$	$1$	$0.004592$	$27.957889$	$0.128395$	$[36,1305,-2547,91264]$	$[9,-51,173,-261,713]$	$[59049/713,-37179/713,14013/713]$	$y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1	713.b	$23 \cdot 31$	$23 \cdot 31$	$0$	$0$	$\Z/9\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.20.2, 3.80.1	✓	✓	$1$	$1$	$1.000000$	$23.149881$	$0.285801$	$[92,73,6379,-91264]$	$[23,19,-41,-326,-713]$	$[-279841/31,-10051/31,943/31]$	$y^2 + (x^3 + x + 1)y = -x^4$
720.a.6480.1	720.a	$2^{4} \cdot 3^{2} \cdot 5$	$- 2^{4} \cdot 3^{4} \cdot 5$	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$0$	2.180.7, 3.90.1	✓	✓	$1$	$2$	$1.000000$	$9.444268$	$0.295133$	$[2360,11992,9047820,25920]$	$[1180,56018,3453120,234166319,6480]$	$[28596971960000/81,1150492082200/81,6677950400/9]$	$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
720.b.116640.1	720.b	$2^{4} \cdot 3^{2} \cdot 5$	$2^{5} \cdot 3^{6} \cdot 5$	$0$	$2$	$\Z/2\Z\oplus\Z/12\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$2$	2.180.3, 3.720.4	✓	✓	$1$	$2^{2} \cdot 3$	$1.000000$	$14.457058$	$0.301189$	$[35416,45688,537039964,466560]$	$[17708,13057938,12831384960,14177105014959,116640]$	$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$	$y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
726.a.1452.1	726.a	$2 \cdot 3 \cdot 11^{2}$	$- 2^{2} \cdot 3 \cdot 11^{2}$	$0$	$1$	$\Z/10\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$3$	$1$	2.60.1, 3.90.1	✓	✓	$1$	$2$	$1.000000$	$15.124086$	$0.302482$	$[760,-69236,-16142609,-5808]$	$[380,17556,702601,-10306189,-1452]$	$[-1980879200000/363,-7297976000/11,-25363896100/363]$	$y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
731.a.12427.1	731.a	$17 \cdot 43$	$- 17^{2} \cdot 43$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$2$	$1.000000$	$14.926779$	$0.298536$	$[480,-21564,-3373785,-49708]$	$[240,5994,167265,1053891,-12427]$	$[-796262400000/12427,-82861056000/12427,-9634464000/12427]$	$y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
741.a.28899.1	741.a	$3 \cdot 13 \cdot 19$	$- 3^{2} \cdot 13^{2} \cdot 19$	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	$2^{2}$	$1.000000$	$18.756843$	$0.293076$	$[576,-840,740385,115596]$	$[288,3596,-38169,-5980972,28899]$	$[220150628352/3211,9544531968/3211,-351765504/3211]$	$y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$
743.a.743.1	743.a	$743$	$-743$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$8$	$0$		✓	✓	$1$	$1$	$0.004577$	$28.765391$	$0.131656$	$[28,1945,15219,95104]$	$[7,-79,-53,-1653,743]$	$[16807/743,-27097/743,-2597/743]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^2$
745.a.745.1	745.a	$5 \cdot 149$	$- 5 \cdot 149$	$0$	$0$	$\Z/9\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.10.1, 3.80.1	✓	✓	$1$	$1$	$1.000000$	$24.572840$	$0.303368$	$[124,1417,38763,95360]$	$[31,-19,39,212,745]$	$[28629151/745,-566029/745,37479/745]$	$y^2 + (x^3 + x + 1)y = -x$
762.a.3048.1	762.a	$2 \cdot 3 \cdot 127$	$- 2^{3} \cdot 3 \cdot 127$	$0$	$1$	$\Z/12\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.15.1, 3.80.1	✓	✓	$1$	$3$	$1.000000$	$16.733449$	$0.348614$	$[428,3169,355487,390144]$	$[107,345,1823,19009,3048]$	$[14025517307/3048,140879945/1016,20871527/3048]$	$y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$

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