| 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 |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 100000.a.200000.1 |
100000.a |
\( 2^{5} \cdot 5^{5} \) |
\( 2^{6} \cdot 5^{5} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.393619\) |
\(4.787238\) |
$[220,-320,-27640,8]$ |
$[1100,55750,4522500,466671875,200000]$ |
$[8052550000,371016250,27361125]$ |
$y^2 + y = 2x^5 + 5x^3 - 10x^2 + 5x - 1$ |
| 100010.a.400040.1 |
100010.a |
\( 2 \cdot 5 \cdot 73 \cdot 137 \) |
\( - 2^{3} \cdot 5 \cdot 73 \cdot 137 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.656191\) |
\(5.872743\) |
\(2.890231\) |
$[10868,-17447,-69073955,-51205120]$ |
$[2717,308314,46839264,8051189423,-400040]$ |
$[-148063561656653357/400040,-3091947885524641/200020,-43221451942812/50005]$ |
$y^2 + (x^3 + 1)y = -x^6 + x^5 + 2x^4 + x^3 - 10x^2 + 2x + 5$ |
| 100017.a.300051.1 |
100017.a |
\( 3^{2} \cdot 11113 \) |
\( 3^{3} \cdot 11113 \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(8.897841\) |
\(2.965947\) |
$[452,-1271,892565,38406528]$ |
$[113,585,-10719,-388368,300051]$ |
$[18424351793/300051,93788305/33339,-5069293/11113]$ |
$y^2 + (x^3 + x + 1)y = x^3 + x - 1$ |
| 100035.a.300105.1 |
100035.a |
\( 3^{4} \cdot 5 \cdot 13 \cdot 19 \) |
\( 3^{5} \cdot 5 \cdot 13 \cdot 19 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.057803\) |
\(13.602351\) |
\(1.572500\) |
$[340,4585,433269,-158080]$ |
$[255,990,-2304,-391905,-300105]$ |
$[-887410625/247,-13510750/247,369920/741]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - 2x + 2$ |
| 100035.b.300105.1 |
100035.b |
\( 3^{4} \cdot 5 \cdot 13 \cdot 19 \) |
\( 3^{5} \cdot 5 \cdot 13 \cdot 19 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.246223\) |
\(15.993195\) |
\(1.968946\) |
$[2492,25801,20659243,158080]$ |
$[1869,135873,12388689,1173246903,300105]$ |
$[93851287159343/1235,3650520528599/1235,534267719209/3705]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^4 - 5x^3 + 11x^2 - 5$ |
| 100036.a.200072.1 |
100036.a |
\( 2^{2} \cdot 89 \cdot 281 \) |
\( 2^{3} \cdot 89 \cdot 281 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.028792\) |
\(14.122440\) |
\(1.219826\) |
$[11236,86545,324737977,25609216]$ |
$[2809,325164,49609856,8405614652,200072]$ |
$[174887470365513049/200072,1801763080537539/50018,48930703272592/25009]$ |
$y^2 + (x^3 + x^2 + 1)y = x^5 - 8x^3 - x^2 + 12x - 6$ |
| 100051.a.700357.1 |
100051.a |
\( 7 \cdot 14293 \) |
\( 7^{2} \cdot 14293 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.056065\) |
\(8.153498\) |
\(0.914251\) |
$[608,50272,6244608,-2801428]$ |
$[304,-4528,78720,857024,-700357]$ |
$[-2596377985024/700357,127211732992/700357,-7274987520/700357]$ |
$y^2 + y = 7x^5 - 4x^4 + 2x^2 - x$ |
| 100059.a.100059.1 |
100059.a |
\( 3 \cdot 33353 \) |
\( - 3 \cdot 33353 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.120355\) |
\(12.224300\) |
\(3.423887\) |
$[136,-1844,-27327,400236]$ |
$[68,500,-2041,-97197,100059]$ |
$[1453933568/100059,157216000/100059,-9437584/100059]$ |
$y^2 + xy = x^5 - x^3 - x$ |
| 100069.a.100069.1 |
100069.a |
\( 100069 \) |
\( 100069 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.210376\) |
\(7.311108\) |
\(1.538080\) |
$[496,5428,942600,400276]$ |
$[248,1658,-7104,-1127689,100069]$ |
$[938120019968/100069,25289460736/100069,-436924416/100069]$ |
$y^2 + x^3y = x^5 + x^4 + 2x^3 + x - 1$ |
| 100076.a.200152.1 |
100076.a |
\( 2^{2} \cdot 127 \cdot 197 \) |
\( 2^{3} \cdot 127 \cdot 197 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.035574\) |
\(13.929680\) |
\(1.486586\) |
$[3940,-86399,-183508255,25619456]$ |
$[985,44026,3775940,445253056,200152]$ |
$[4706682753125/1016,106787814625/508,4649126125/254]$ |
$y^2 + (x^3 + x + 1)y = -6x^4 + 10x^3 - 2x^2$ |
| 100082.a.800656.1 |
100082.a |
\( 2 \cdot 163 \cdot 307 \) |
\( - 2^{4} \cdot 163 \cdot 307 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026991\) |
\(14.653381\) |
\(1.582047\) |
$[8760,105132,295938975,-3202624]$ |
$[4380,781828,182944825,47510827979,-800656]$ |
$[-100751279419800000/50041,-4105949171526000/50041,-219355418795625/50041]$ |
$y^2 + (x^3 + x)y = -7x^4 + 26x^2 - 29x + 9$ |
| 100089.a.100089.1 |
100089.a |
\( 3^{3} \cdot 11 \cdot 337 \) |
\( 3^{3} \cdot 11 \cdot 337 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.106187\) |
\(14.805872\) |
\(1.572193\) |
$[252,11745,848655,-12811392]$ |
$[63,-324,-2644,-67887,-100089]$ |
$[-36756909/3707,3000564/3707,388668/3707]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^4 - 2x^2 + x$ |
| 100096.a.100096.1 |
100096.a |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.616386\) |
\(0.904096\) |
$[450,2088,442170,391]$ |
$[900,28182,-64820,-213140781,100096]$ |
$[2306601562500/391,160505296875/782,-820378125/1564]$ |
$y^2 = x^5 - 2x^4 - 3x^3 - 7x^2 - 7x - 2$ |
| 100096.b.100096.1 |
100096.b |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.972917\) |
\(1.743229\) |
$[1326,-1344,-597342,-391]$ |
$[2652,296630,44782996,7693787123,-100096]$ |
$[-30142461298716/23,-2542592373165/46,-289488481893/92]$ |
$y^2 = x^5 - 9x^3 + 5x^2 + 21x - 20$ |
| 100096.c.100096.1 |
100096.c |
\( 2^{8} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 17 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.273964\) |
\(2.818491\) |
$[1326,-1344,-597342,-391]$ |
$[2652,296630,44782996,7693787123,-100096]$ |
$[-30142461298716/23,-2542592373165/46,-289488481893/92]$ |
$y^2 = x^5 - 9x^3 - 5x^2 + 21x + 20$ |
| 100109.a.100109.1 |
100109.a |
\( 100109 \) |
\( 100109 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.175804\) |
\(8.513439\) |
\(1.496696\) |
$[248,-176,42904,400436]$ |
$[124,670,-1364,-154509,100109]$ |
$[29316250624/100109,1277438080/100109,-20972864/100109]$ |
$y^2 + y = x^5 + 2x^4 + 3x^3 + x^2 + x$ |
| 100121.a.100121.1 |
100121.a |
\( 7 \cdot 14303 \) |
\( 7 \cdot 14303 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.102837\) |
\(12.424832\) |
\(1.277731\) |
$[164,-11999,-624847,12815488]$ |
$[41,570,3144,-48999,100121]$ |
$[115856201/100121,39284970/100121,5285064/100121]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^2$ |
| 100121.b.700847.1 |
100121.b |
\( 7 \cdot 14303 \) |
\( 7^{2} \cdot 14303 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.033092\) |
\(14.435395\) |
\(0.955379\) |
$[1820,71209,42800059,-89708416]$ |
$[455,5659,-1397,-8164979,-700847]$ |
$[-397979684375/14303,-10878720125/14303,5902325/14303]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 3x^2 + 6x + 4$ |
| 100124.a.400496.1 |
100124.a |
\( 2^{2} \cdot 25031 \) |
\( - 2^{4} \cdot 25031 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.822181\) |
\(11.147614\) |
\(2.291339\) |
$[124,-15239,104995,51263488]$ |
$[31,675,-6857,-167048,400496]$ |
$[28629151/400496,20108925/400496,-6589577/400496]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^2 - 2x$ |
| 100128.a.801024.1 |
100128.a |
\( 2^{5} \cdot 3 \cdot 7 \cdot 149 \) |
\( 2^{8} \cdot 3 \cdot 7 \cdot 149 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(0.725352\) |
\(1.450704\) |
$[8464,2155228,4957700868,3204096]$ |
$[4232,387038,46859332,12127569895,801024]$ |
$[5302593435347072/3129,114591028813564/3129,3278290581553/3129]$ |
$y^2 + (x^2 + 1)y = 4x^5 - x^4 - 13x^3 - 2x^2 + 7x - 2$ |
| 100130.a.200260.1 |
100130.a |
\( 2 \cdot 5 \cdot 17 \cdot 19 \cdot 31 \) |
\( - 2^{2} \cdot 5 \cdot 17 \cdot 19 \cdot 31 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.128156\) |
\(18.886321\) |
\(1.210199\) |
$[532,218185,-1085371,-25633280]$ |
$[133,-8354,356384,-5597561,-200260]$ |
$[-2190305047/10540,517208671/5270,-82948376/2635]$ |
$y^2 + (x^2 + x + 1)y = x^6 + 5x^5 + 6x^4 + x^2 + x$ |
| 100152.a.600912.1 |
100152.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 107 \) |
\( - 2^{4} \cdot 3^{3} \cdot 13 \cdot 107 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.020121\) |
\(11.020777\) |
\(1.330500\) |
$[88,-1235,-14387,75114]$ |
$[88,1146,-5760,-455049,600912]$ |
$[329832448/37557,16270144/12519,-309760/4173]$ |
$y^2 + y = x^6 - 2x^5 - 6x^4 - 4x^3 + x$ |
| 100154.a.200308.1 |
100154.a |
\( 2 \cdot 50077 \) |
\( 2^{2} \cdot 50077 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.051351\) |
\(13.921948\) |
\(1.429825\) |
$[104,5080,134677,-801232]$ |
$[52,-734,-2409,-166006,-200308]$ |
$[-95051008/50077,25801568/50077,1628484/50077]$ |
$y^2 + (x + 1)y = x^6 + x^5 + 2x^4 + 3x^3 + x^2$ |
| 100154.b.200308.1 |
100154.b |
\( 2 \cdot 50077 \) |
\( 2^{2} \cdot 50077 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(4.011604\) |
\(2.005802\) |
$[584,-896,-367069,801232]$ |
$[292,3702,86305,2874064,200308]$ |
$[530706327808/50077,23042254944/50077,1839677380/50077]$ |
$y^2 + (x + 1)y = x^5 + x^3 - 5x^2 + 3x - 1$ |
| 100162.a.100162.1 |
100162.a |
\( 2 \cdot 61 \cdot 821 \) |
\( - 2 \cdot 61 \cdot 821 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.174345\) |
\(6.880814\) |
\(1.199636\) |
$[21396,-10503,-75948435,-12820736]$ |
$[5349,1192596,354674332,118716945663,-100162]$ |
$[-4378879451923801749/100162,-91260143303221602/50081,-5073935703495966/50081]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 9x^3 + 8x^2 + 20x - 20$ |
| 100162.b.400648.1 |
100162.b |
\( 2 \cdot 61 \cdot 821 \) |
\( - 2^{3} \cdot 61 \cdot 821 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.772491\) |
\(11.205131\) |
\(2.885289\) |
$[3652,-232031,-299933231,-51282944]$ |
$[913,44400,3475524,300448353,-400648]$ |
$[-634386434595793/400648,-4223819158350/50081,-724272266289/100162]$ |
$y^2 + (x^2 + x)y = x^5 - 4x^4 + 4x^2 + 5x + 2$ |
| 100224.a.601344.1 |
100224.a |
\( 2^{7} \cdot 3^{3} \cdot 29 \) |
\( 2^{8} \cdot 3^{4} \cdot 29 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.501426\) |
\(5.342535\) |
\(2.678888\) |
$[72,648,17784,2349]$ |
$[144,-864,-50432,-2002176,601344]$ |
$[2985984/29,-124416/29,-50432/29]$ |
$y^2 = x^5 + 2x^4 + 4x^3 + 2x^2 + x - 1$ |
| 100224.b.601344.1 |
100224.b |
\( 2^{7} \cdot 3^{3} \cdot 29 \) |
\( 2^{8} \cdot 3^{4} \cdot 29 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.191301\) |
\(10.211931\) |
\(1.953550\) |
$[120,1368,38520,-2349]$ |
$[240,-1248,1280,-312576,-601344]$ |
$[-38400000/29,832000/29,-32000/261]$ |
$y^2 = x^5 + x^4 - 2x^3 + 4x^2 - 2x + 1$ |
| 100227.a.902043.1 |
100227.a |
\( 3 \cdot 33409 \) |
\( - 3^{3} \cdot 33409 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.051324\) |
\(7.555720\) |
\(1.163380\) |
$[7648,-11120,-25359504,-3608172]$ |
$[3824,611144,130289488,31182503344,-902043]$ |
$[-817691377217306624/902043,-34174109226336256/902043,-1905220056076288/902043]$ |
$y^2 + y = x^5 + x^4 + 23x^2 + 57x + 36$ |
| 100234.a.801872.1 |
100234.a |
\( 2 \cdot 23 \cdot 2179 \) |
\( 2^{4} \cdot 23 \cdot 2179 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.125507\) |
\(5.600760\) |
\(1.405864\) |
$[2096,-1976,-780241,3207488]$ |
$[1048,46092,2655225,164550834,801872]$ |
$[79010794805248/50117,144165579648/2179,182265264900/50117]$ |
$y^2 + (x^3 + x)y = x^5 - x^4 - 5x^3 - x^2 + 5x - 3$ |
| 100240.a.400960.1 |
100240.a |
\( 2^{4} \cdot 5 \cdot 7 \cdot 179 \) |
\( 2^{6} \cdot 5 \cdot 7 \cdot 179 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.061812\) |
\(6.806169\) |
\(2.103531\) |
$[3092,3169,3251369,50120]$ |
$[3092,396240,67352576,12812006848,400960]$ |
$[4415881923441488/6265,36603852142416/1253,10061279346176/6265]$ |
$y^2 + x^3y = x^5 - x^4 - 5x^3 + 6x^2 + 10x - 15$ |
| 100261.a.100261.1 |
100261.a |
\( 7 \cdot 14323 \) |
\( - 7 \cdot 14323 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.215449\) |
\(6.839751\) |
\(1.473618\) |
$[7048,-31736,-73311541,-401044]$ |
$[3524,522730,104271441,23551476296,-100261]$ |
$[-543474909254042624/100261,-22876265307259520/100261,-1294902814688016/100261]$ |
$y^2 + (x + 1)y = x^5 - 16x^4 - x^3 + 7x^2 - 3x$ |
| 100261.b.100261.1 |
100261.b |
\( 7 \cdot 14323 \) |
\( - 7 \cdot 14323 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.095729\) |
\(16.886745\) |
\(1.616555\) |
$[592,-620,494801,401044]$ |
$[296,3754,-3441,-3777763,100261]$ |
$[2272262782976/100261,97357497344/100261,-301486656/100261]$ |
$y^2 + xy = x^5 - x^4 + 3x^2 - 5x + 2$ |
| 100277.a.100277.1 |
100277.a |
\( 149 \cdot 673 \) |
\( 149 \cdot 673 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067136\) |
\(18.915020\) |
\(1.269881\) |
$[452,20449,572017,12835456]$ |
$[113,-320,22140,599855,100277]$ |
$[18424351793/100277,-461727040/100277,282705660/100277]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 + 3x^3 - x^2 - x$ |
| 100277.b.100277.1 |
100277.b |
\( 149 \cdot 673 \) |
\( 149 \cdot 673 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.063459\) |
\(5.063459\) |
$[24088,9051808,81756374264,401108]$ |
$[12044,4535446,7341036,-5120463745333,100277]$ |
$[253427496970010676224/100277,7923776934359848064/100277,1064875530261696/100277]$ |
$y^2 + y = x^5 + x^4 - 19x^3 - 11x^2 + 92x + 13$ |
| 100277.c.100277.1 |
100277.c |
\( 149 \cdot 673 \) |
\( 149 \cdot 673 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.169546\) |
\(14.812084\) |
\(2.511336\) |
$[704,5824,1359616,401108]$ |
$[352,4192,44800,-450816,100277]$ |
$[5403974828032/100277,182830759936/100277,5550899200/100277]$ |
$y^2 + y = x^5 - 4x^4 + 4x^2 - 2x$ |
| 100278.a.200556.1 |
100278.a |
\( 2 \cdot 3^{4} \cdot 619 \) |
\( - 2^{2} \cdot 3^{4} \cdot 619 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.165292\) |
\(7.453400\) |
\(2.463980\) |
$[17256,37404,223081551,-802224]$ |
$[8628,3095532,1476933817,790166652513,-200556]$ |
$[-147572580633292032/619,-6136499412390336/619,-3054068731880548/5571]$ |
$y^2 + x^2y = 2x^5 + 9x^4 + x^3 - 21x^2 + 15x - 3$ |
| 100283.a.100283.1 |
100283.a |
\( 17^{2} \cdot 347 \) |
\( - 17^{2} \cdot 347 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.132804\) |
\(12.727828\) |
\(1.690312\) |
$[112,-1904,-19159,401132]$ |
$[56,448,-2401,-83790,100283]$ |
$[550731776/100283,78675968/100283,-7529536/100283]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - x^3 - x$ |
| 100293.a.902637.1 |
100293.a |
\( 3 \cdot 101 \cdot 331 \) |
\( - 3^{3} \cdot 101 \cdot 331 \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(4.422795\) |
\(2.948530\) |
$[5020,150745,235520883,115537536]$ |
$[1255,59345,3494111,215820070,902637]$ |
$[3113283207034375/902637,117304672574375/902637,5503312177775/902637]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + x^5 - 5x^4 + 3x^3 - 7x^2 + 2x - 2$ |
| 100309.a.100309.1 |
100309.a |
\( 11^{2} \cdot 829 \) |
\( 11^{2} \cdot 829 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.471800\) |
\(2.617950\) |
$[256,-1880,-101225,401236]$ |
$[128,996,4961,-89252,100309]$ |
$[34359738368/100309,2088763392/100309,671744/829]$ |
$y^2 + xy = x^5 + 2x^3 - 3x^2 + x$ |
| 100312.a.200624.1 |
100312.a |
\( 2^{3} \cdot 12539 \) |
\( - 2^{4} \cdot 12539 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.298724\) |
\(2.649362\) |
$[224,4432,1358180,802496]$ |
$[112,-216,-124676,-3502592,200624]$ |
$[1101463552/12539,-18966528/12539,-97745984/12539]$ |
$y^2 + (x^2 + 1)y = -x^6 - 2x^5 + x^4 + 3x^3 - x - 1$ |
| 100315.a.501575.1 |
100315.a |
\( 5 \cdot 20063 \) |
\( - 5^{2} \cdot 20063 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.052093\) |
\(14.989420\) |
\(1.561682\) |
$[4380,252849,473905527,64201600]$ |
$[1095,39424,-338316,-481176949,501575]$ |
$[62969549637375/20063,2070441838080/20063,-16225973676/20063]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 + 3x^4 + x^3 + 2x^2 - 5x + 1$ |
| 100317.a.702219.1 |
100317.a |
\( 3 \cdot 7 \cdot 17 \cdot 281 \) |
\( - 3 \cdot 7^{2} \cdot 17 \cdot 281 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.346453\) |
\(8.322593\) |
\(1.441696\) |
$[7032,-686316,-1600461345,-2808876]$ |
$[3516,629480,166727073,47491829567,-702219]$ |
$[-179111337635976192/234073,-9120261286863360/234073,-687040919518896/234073]$ |
$y^2 + (x^2 + 1)y = x^5 - 10x^3 - 10x^2 + 28x + 38$ |
| 100325.a.100325.1 |
100325.a |
\( 5^{2} \cdot 4013 \) |
\( 5^{2} \cdot 4013 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.396628\) |
\(7.575309\) |
\(3.004578\) |
$[416,4420,595015,401300]$ |
$[208,1066,-2719,-425477,100325]$ |
$[389328928768/100325,9592840192/100325,-117634816/100325]$ |
$y^2 + x^2y = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$ |
| 100325.b.100325.1 |
100325.b |
\( 5^{2} \cdot 4013 \) |
\( 5^{2} \cdot 4013 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.093538\) |
\(13.292801\) |
\(1.243385\) |
$[3060,-200871,-238360131,12841600]$ |
$[765,32754,2568348,222990426,100325]$ |
$[10480141999125/4013,586554865290/4013,60122458332/4013]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 3x^4 - 10x^2 + 2x + 8$ |
| 100341.a.100341.1 |
100341.a |
\( 3^{2} \cdot 11149 \) |
\( 3^{2} \cdot 11149 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.949761\) |
\(4.057160\) |
\(3.853333\) |
$[416,5584,670128,-401364]$ |
$[208,872,144,-182608,-100341]$ |
$[-389328928768/100341,-7847051264/100341,-692224/11149]$ |
$y^2 + y = x^5 - x^4 - 4x^3 - 5x^2 - 3x - 1$ |
| 100352.a.100352.1 |
100352.a |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$2$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.501978\) |
\(2.125494\) |
$[56,-80,-404,392]$ |
$[112,736,-512,-149760,100352]$ |
$[175616,10304,-64]$ |
$y^2 = x^5 - x^4 + x^2 + x$ |
| 100352.b.100352.1 |
100352.b |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.137847\) |
\(2.034462\) |
$[342,2436,250236,392]$ |
$[684,12998,195556,-8796925,100352]$ |
$[146211169851/98,32496371289/784,1429563249/1568]$ |
$y^2 = x^5 + x^4 - 5x^3 - 2x^2 + 4x - 1$ |
| 100352.c.100352.1 |
100352.c |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.026921\) |
\(10.319985\) |
\(2.649452\) |
$[1046,1036,356188,392]$ |
$[2092,179590,20265956,2535952963,100352]$ |
$[39129873538843/98,12845683618265/784,1385831669681/1568]$ |
$y^2 = x^5 - 9x^3 + 7x^2 + 14x - 14$ |
| 100352.d.100352.1 |
100352.d |
\( 2^{11} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.695932\) |
\(11.589322\) |
\(2.016345\) |
$[304,1372,149940,392]$ |
$[608,11744,71936,-23546112,100352]$ |
$[40568406016/49,1288833536/49,12984448/49]$ |
$y^2 = x^5 - x^4 - 4x^3 + 3x^2 + 4x - 2$ |
