LMFDB - Genus 2 curve search results

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Conductor	Absolute discriminant	Rational points*	Weierstrass points	Torsion order

Bad $p$	2-Selmer rank	Analytic rank*	Analytic Ш*	Torsion

$\Q$ -end algebra	$\mathrm{ST}(X)$	$\mathrm{Aut}(X)$	Square Ш*	$\overline{\Q}$ -simple

$\overline{\Q}$ -end algebra	$\mathrm{ST}^0(X)$	$\mathrm{Aut}(X_{\overline{\Q}})$	Locally solvable	$\GL_2$ -type

Galois image	Nonmax $\ \ell$

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Results (40 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	✓	✓	$1$	$2$	$1.000000$	$26.841829$	$0.134209$	$[26,-2,40,2]$	$[52,118,-36,-3949,512]$	$[742586,129623/4,-1521/8]$	$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
324.a.648.1	324.a	$2^{2} \cdot 3^{4}$	$- 2^{3} \cdot 3^{4}$	$0$	$0$	$\Z/21\Z$	$\mathrm{M}_2(\Q)$	$\mathsf{CM}$	✓	$E_3$		✓		$C_6$	$D_6$	$6$	$0$	2.40.3, 3.1920.3	✓	✓	$1$	$3$	$1.000000$	$25.521769$	$0.173617$	$[60,945,2295,82944]$	$[15,-30,140,300,648]$	$[9375/8,-625/4,875/18]$	$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
388.a.776.1	388.a	$2^{2} \cdot 97$	$2^{3} \cdot 97$	$0$	$0$	$\Z/21\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3,7$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.10.1, 3.80.1	✓	✓	$1$	$3$	$1.000000$	$29.135501$	$0.198201$	$[36,1569,-13743,99328]$	$[9,-62,356,-160,776]$	$[59049/776,-22599/388,7209/194]$	$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$
472.a.944.1	472.a	$2^{3} \cdot 59$	$- 2^{4} \cdot 59$	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	$2$	$1.000000$	$29.113273$	$0.227447$	$[280,760,60604,-3776]$	$[140,690,4544,40015,-944]$	$[-3361400000/59,-118335000/59,-5566400/59]$	$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$
476.a.952.1	476.a	$2^{2} \cdot 7 \cdot 17$	$- 2^{3} \cdot 7 \cdot 17$	$0$	$1$	$\Z/3\Z\oplus\Z/6\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.90.1, 3.5760.3	✓	✓	$1$	$3$	$1.000000$	$26.722339$	$0.247429$	$[7340,1042345,2905273355,121856]$	$[1835,96870,-3910340,-4139817700,952]$	$[20805604708146875/952,299272981175625/476,-27661753375/2]$	$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
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	✓	✓	$1$	$1$	$1.000000$	$30.060256$	$0.248432$	$[284,2401,246639,-67712]$	$[71,110,-624,-14101,-529]$	$[-1804229351/529,-39370210/529,3145584/529]$	$y^2 + (x^3 + x + 1)y = -x^5$
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	✓	✓	$1$	$1$	$1.000000$	$22.396252$	$0.223963$	$[68,124,2616,72]$	$[68,110,-36,-3637,576]$	$[22717712/9,540430/9,-289]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
587.a.587.1	587.a	$587$	$587$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	$1$	$0.003773$	$29.510964$	$0.111352$	$[60,1401,54147,-75136]$	$[15,-49,-501,-2479,-587]$	$[-759375/587,165375/587,112725/587]$	$y^2 + (x^3 + x + 1)y = -x^2 - x$
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	✓	✓	$1$	$1$	$1.000000$	$14.411617$	$0.294115$	$[120,192,9912,2388]$	$[60,118,-68,-4501,597]$	$[259200000/199,8496000/199,-81600/199]$	$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
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	✓	✓	$1$	$1$	$1.000000$	$26.910016$	$0.269100$	$[176,148,7375,-2412]$	$[88,298,1361,7741,-603]$	$[-5277319168/603,-203078656/603,-10539584/603]$	$y^2 + (x^2 + 1)y = x^5 - x^3 + x$
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	✓	✓	$1$	$1$	$1.000000$	$11.491655$	$0.319213$	$[420,4305,640185,87808]$	$[105,280,-980,-45325,686]$	$[37209375/2,472500,-15750]$	$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
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	✓	✓	$1$	$1$	$1.000000$	$18.812569$	$0.293946$	$[104,-824,-20333,-2764]$	$[52,250,601,-7812,-691]$	$[-380204032/691,-35152000/691,-1625104/691]$	$y^2 + (x + 1)y = x^5 - x^3 - x^2$
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	✓	✓	$1$	$1$	$1.000000$	$23.149881$	$0.285801$	$[92,73,6379,-91264]$	$[23,19,-41,-326,-713]$	$[-279841/31,-10051/31,943/31]$	$y^2 + (x^3 + x + 1)y = -x^4$
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	✓	✓	$1$	$1$	$1.000000$	$24.572840$	$0.303368$	$[124,1417,38763,95360]$	$[31,-19,39,212,745]$	$[28629151/745,-566029/745,37479/745]$	$y^2 + (x^3 + x + 1)y = -x$
763.a.763.1	763.a	$7 \cdot 109$	$- 7 \cdot 109$	$0$	$1$	$\Z/10\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$30.485750$	$0.304858$	$[216,1116,75735,-3052]$	$[108,300,81,-20313,-763]$	$[-14693280768/763,-377913600/763,-944784/763]$	$y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x$
797.a.797.1	797.a	$797$	$797$	$0$	$0$	$\Z/7\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	$1$	$1.000000$	$17.440989$	$0.355939$	$[24,528,7608,3188]$	$[12,-82,-548,-3325,797]$	$[248832/797,-141696/797,-78912/797]$	$y^2 + y = x^5 - x^4 + x^3$
832.a.832.1	832.a	$2^{6} \cdot 13$	$- 2^{6} \cdot 13$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	$1$	$1.000000$	$21.148215$	$0.330441$	$[272,-131,-12402,-104]$	$[272,3170,51008,956319,-832]$	$[-23262937088/13,-996749440/13,-58965248/13]$	$y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$
841.a.841.1	841.a	$29^{2}$	$- 29^{2}$	$0$	$0$	$\Z/7\Z$	$\mathsf{RM}$	$\mathsf{RM}$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$2$	$0$	2.60.2, 3.72.2	✓	✓	$1$	$1$	$1.000000$	$14.284557$	$0.291522$	$[1420,4201,1973899,107648]$	$[355,5076,93408,1848516,841]$	$[5638216721875/841,227094529500/841,11771743200/841]$	$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$
847.a.847.1	847.a	$7 \cdot 11^{2}$	$- 7 \cdot 11^{2}$	$1$	$1$	$\Z/5\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.15.2, 3.90.1	✓	✓	$1$	$1$	$0.196056$	$20.305961$	$0.159244$	$[120,276,6864,3388]$	$[60,104,504,4856,847]$	$[777600000/847,22464000/847,259200/121]$	$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
847.d.847.1	847.d	$7 \cdot 11^{2}$	$- 7 \cdot 11^{2}$	$0$	$1$	$\Z/3\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.15.2, 3.720.4			$2$	$1$	$1.000000$	$1.179535$	$0.262119$	$[80408,402403732,8094753026048,3388]$	$[40204,281112,1967560,19956424,847]$	$[105037970421355597057024/847,18267839107785466368/847,454326923025280/121]$	$y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$
862.a.862.1	862.a	$2 \cdot 431$	$- 2 \cdot 431$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$2$	$0$	2.15.1	✓	✓	$1$	$1$	$1.000000$	$23.926605$	$0.373853$	$[1940,2609665,270472593,-110336]$	$[485,-98935,11156681,-1094285985,-862]$	$[-26835438303125/862,11286912906875/862,-2624330288225/862]$	$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$
862.b.862.1	862.b	$2 \cdot 431$	$2 \cdot 431$	$0$	$0$	$\Z/9\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1, 3.80.1	✓	✓	$1$	$1$	$1.000000$	$27.488991$	$0.339370$	$[552,696,112755,3448]$	$[276,3058,45033,769436,862]$	$[800784050688/431,32146576704/431,1715216904/431]$	$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$
893.a.893.1	893.a	$19 \cdot 47$	$19 \cdot 47$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$8$	$0$		✓	✓	$1$	$1$	$0.006429$	$23.402435$	$0.150459$	$[156,-519,-11805,-114304]$	$[39,85,67,-1153,-893]$	$[-90224199/893,-5042115/893,-101907/893]$	$y^2 + (x^3 + x + 1)y = -x^4 - x^2$
909.a.909.1	909.a	$3^{2} \cdot 101$	$3^{2} \cdot 101$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$21.805548$	$0.340712$	$[40,-200,-5469,3636]$	$[20,50,441,1580,909]$	$[3200000/909,400000/909,19600/101]$	$y^2 + (x^3 + x)y = -x^4 + x^2 - x$
925.a.925.1	925.a	$5^{2} \cdot 37$	$5^{2} \cdot 37$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$20.878934$	$0.326233$	$[40,-944,-14117,3700]$	$[20,174,713,-4004,925]$	$[128000/37,55680/37,11408/37]$	$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$
930.a.930.1	930.a	$2 \cdot 3 \cdot 5 \cdot 31$	$2 \cdot 3 \cdot 5 \cdot 31$	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	$\Q \times \Q$	$\Q \times \Q$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.180.3, 3.90.1	✓	✓	$1$	$1$	$1.000000$	$24.846489$	$0.388226$	$[46596,239073,3674852529,119040]$	$[11649,5644172,3640360380,2637470125259,930]$	$[71502622649365111083/310,1487013548016809538/155,531176338621566]$	$y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
953.a.953.1	953.a	$953$	$-953$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$0$	2.10.1	✓	✓	$1$	$1$	$0.006276$	$24.886682$	$0.156194$	$[92,1513,26203,121984]$	$[23,-41,67,-35,953]$	$[6436343/953,-498847/953,35443/953]$	$y^2 + (x^3 + x + 1)y = x^3 + x^2$
961.a.961.1	961.a	$31^{2}$	$- 31^{2}$	$0$	$1$	$\mathsf{trivial}$	$\mathsf{RM}$	$\mathsf{RM}$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$0$	$0$	2.15.2, 3.72.2			$2$	$1$	$1.000000$	$0.224644$	$0.449288$	$[66980,1011437281,14016353908561,-123008]$	$[16745,-30460094,12221475912,-180792178085599,-961]$	$[-1316514841399349215625/961,143016680917998700750/961,-3426841043882137800/961]$	$y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$
961.a.961.2	961.a	$31^{2}$	$- 31^{2}$	$0$	$1$	$\Z/5\Z$	$\mathsf{RM}$	$\mathsf{RM}$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$0$	$0$	2.15.2, 3.72.2			$2$	$1$	$1.000000$	$5.616097$	$0.449288$	$[11260,503521,1770579599,123008]$	$[2815,309196,43449708,6677190401,961]$	$[176763257309509375/961,6897140364776500/961,344305262376300/961]$	$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$
961.a.961.3	961.a	$31^{2}$	$31^{2}$	$0$	$0$	$\Z/5\Z$	$\mathsf{RM}$	$\mathsf{RM}$	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$2$	$0$	2.120.2, 3.72.2	✓	✓	$1$	$1$	$1.000000$	$11.232193$	$0.449288$	$[260,1681,185209,123008]$	$[65,106,-672,-13729,961]$	$[1160290625/961,29110250/961,-2839200/961]$	$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$
971.a.971.1	971.a	$971$	$-971$	$1$	$1$	$\mathsf{trivial}$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	$1$	$0.005970$	$29.647111$	$0.176998$	$[256,1024,80304,-3884]$	$[128,512,2000,-1536,-971]$	$[-34359738368/971,-1073741824/971,-32768000/971]$	$y^2 + y = x^5 - 2x^3 + x$
997.a.997.1	997.a	$997$	$997$	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	$1$	$1.000000$	$21.589621$	$0.337338$	$[6112,48064,98113399,3988]$	$[3056,381120,61964417,11027700988,997]$	$[266542673508171776/997,10877317101649920/997,578694117523712/997]$	$y^2 + xy = x^5 - 8x^4 + 16x^3 - x$
997.a.997.2	997.a	$997$	$997$	$0$	$1$	$\Z/8\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	$1$	$1.000000$	$21.589621$	$0.337338$	$[64,184,391,3988]$	$[32,12,305,2404,997]$	$[33554432/997,393216/997,312320/997]$	$y^2 + (x + 1)y = x^5 + x^4$
997.b.997.1	997.b	$997$	$997$	$1$	$1$	$\Z/3\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1, 3.80.1	✓	✓	$1$	$1$	$0.081270$	$19.932843$	$0.179992$	$[32,16,-1680,-3988]$	$[16,8,208,816,-997]$	$[-1048576/997,-32768/997,-53248/997]$	$y^2 + y = x^5 - 2x^4 + 2x^3 - x^2$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.