| 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 |
| 13696.b.109568.1 |
13696.b |
\( 2^{7} \cdot 107 \) |
\( - 2^{10} \cdot 107 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.378973\) |
\(1.705378\) |
$[122264,117761944,4373366507708,-13696]$ |
$[122264,544345608,3009566254336,17912366892811760,-109568]$ |
$[-26680443465746439572576/107,-971562104378078994348/107,-43934041117291009744/107]$ |
$y^2 + x^2y = x^5 + 12x^4 - 2x^3 - 253x^2 + 288x - 83$ |
| 16108.b.64432.1 |
16108.b |
\( 2^{2} \cdot 4027 \) |
\( 2^{4} \cdot 4027 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 5 \) |
\(1.000000\) |
\(1.145759\) |
\(2.062367\) |
$[140828,1269640849,44520371520391,-8247296]$ |
$[35207,-1254500,44515616,-1627239372,-64432]$ |
$[-54093502359788249792807/64432,13686668079248773375/16108,-3448660520341874/4027]$ |
$y^2 + (x^2 + x)y = 2x^5 - 32x^4 + 55x^3 - 79x^2 + 49x - 25$ |
| 19201.a.134407.1 |
19201.a |
\( 7 \cdot 13 \cdot 211 \) |
\( - 7^{2} \cdot 13 \cdot 211 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.515812\) |
\(2.321155\) |
$[89812,548899033,12142386323293,-17204096]$ |
$[22453,-1865076,201909152,263739426020,-134407]$ |
$[-5706527070413547267493/134407,21111527759456884452/134407,-101789916360836768/134407]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 23x^4 - 34x^3 + 10x^2 + 14x - 7$ |
| 22324.b.178592.1 |
22324.b |
\( 2^{2} \cdot 5581 \) |
\( 2^{5} \cdot 5581 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.80.2 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.385657\) |
\(1.735456\) |
$[680068,28110905545,4801389439684597,22859776]$ |
$[170017,33119781,6473494233,921043881000,178592]$ |
$[142056707049989927994269857/178592,162766304179903139074053/178592,187121402001206573337/178592]$ |
$y^2 + (x^2 + x)y = x^5 - 37x^4 + 232x^3 - 407x^2 - 4x$ |
| 32119.a.32119.1 |
32119.a |
\( 32119 \) |
\( 32119 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.357952\) |
\(3.221565\) |
$[46964,147959497,1716344218693,4111232]$ |
$[11741,-421184,14829864,-819632158,32119]$ |
$[223113289976409774701/32119,-681690322946572864/32119,2044312783482984/32119]$ |
$y^2 + (x^2 + x + 1)y = -x^6 - 4x^5 + 4x^4 + 23x^3 - 21x^2 - 9x - 1$ |
| 50608.b.809728.1 |
50608.b |
\( 2^{4} \cdot 3163 \) |
\( - 2^{8} \cdot 3163 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.891559\) |
\(2.006007\) |
$[4280,961120,1057109684,-3163]$ |
$[8560,490080,28891136,1782429440,-809728]$ |
$[-179526621529600000/3163,-1200738146880000/3163,-8269365401600/3163]$ |
$y^2 = x^5 - 30x^3 - 72x^2 - 28x - 3$ |
| 59648.b.59648.1 |
59648.b |
\( 2^{8} \cdot 233 \) |
\( - 2^{8} \cdot 233 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.427588\) |
\(3.848289\) |
$[133712,73216630,3060111036018,-7456]$ |
$[133712,696143036,4626703843088,33507674423921340,-59648]$ |
$[-166959816524855023849472/233,-6500842917098124952768/233,-323126447087448378512/233]$ |
$y^2 + (x^2 + 1)y = x^5 + 17x^4 + 55x^3 - 179x^2 - 14x + 1$ |
| 64000.c.64000.1 |
64000.c |
\( 2^{9} \cdot 5^{3} \) |
\( 2^{9} \cdot 5^{3} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.36.1, 3.2160.6 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.339675\) |
\(3.057078\) |
$[5400,-58611570,-137361090600,8000]$ |
$[5400,40289380,63851677200,-319608770976100,64000]$ |
$[71744535000000,99126983317500,29092420424250]$ |
$y^2 + x^2y = x^5 - 10x^3 + 75x^2 + 60x - 665$ |
| 73990.a.369950.1 |
73990.a |
\( 2 \cdot 5 \cdot 7^{2} \cdot 151 \) |
\( - 2 \cdot 5^{2} \cdot 7^{2} \cdot 151 \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.720.4 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(1.978775\) |
\(3.957549\) |
$[214768,280489420,21659750402223,-1479800]$ |
$[107384,433723574,1854197074625,2748740004549381,-369950]$ |
$[-7139501517373128431091712/184975,-268535535102198797838848/184975,-8727080089252997920/151]$ |
$y^2 + xy = 5x^5 - 21x^4 - 22x^3 + 89x^2 + 104x + 14$ |
| 92572.a.92572.1 |
92572.a |
\( 2^{2} \cdot 23143 \) |
\( 2^{2} \cdot 23143 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.113660\) |
\(1.022943\) |
$[487396,14554718569,1779328866322245,11849216]$ |
$[121849,12185843,1227329537,263526783316,92572]$ |
$[26860237392090704873884249/92572,22045577829284388595307/92572,18222381083587545137/92572]$ |
$y^2 + (x^2 + x)y = x^5 - 32x^4 + 96x^3 + 23x^2 - 169x - 89$ |
| 96347.b.96347.1 |
96347.b |
\( 23 \cdot 59 \cdot 71 \) |
\( - 23 \cdot 59 \cdot 71 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.502679\) |
\(4.524108\) |
$[49240,152172544,1871930206648,-385388]$ |
$[24620,-106074,893228,2684894971,-96347]$ |
$[-9045659648496483200000/96347,22295373041232000/1357,-23540223918400/4189]$ |
$y^2 + y = -18x^6 - 41x^5 + x^4 + 35x^3 - 5x - 1$ |
| 98091.b.686637.1 |
98091.b |
\( 3^{4} \cdot 7 \cdot 173 \) |
\( 3^{4} \cdot 7^{2} \cdot 173 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.563345\) |
\(2.535051\) |
$[315732,6174225081,488084468735277,87889536]$ |
$[78933,2341392,67943920,-29774765076,686637]$ |
$[37827533773124068057653/8477,14215591635215839184/8477,47035450598126320/76293]$ |
$y^2 + (x^2 + x + 1)y = 7x^5 - 69x^4 - 95x^3 - 16x^2 + 9x - 1$ |
| 102591.b.307773.1 |
102591.b |
\( 3^{2} \cdot 11399 \) |
\( 3^{3} \cdot 11399 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.239128\) |
\(4.304299\) |
$[51384,185719536,2337338192904,1231092]$ |
$[25692,-3449970,455183548,-51929321421,307773]$ |
$[414596663308308796416/11399,-2166932056945495680/11399,33384115475036608/34197]$ |
$y^2 + y = x^5 - 79x^4 + 123x^3 - 62x^2 + 11x - 1$ |
| 134656.d.134656.1 |
134656.d |
\( 2^{9} \cdot 263 \) |
\( - 2^{9} \cdot 263 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.444929\) |
\(4.004360\) |
$[1404352,61964662,28843963385776,-16832]$ |
$[1404352,82133879388,6401747508897792,561083193573275184060,-134656]$ |
$[-10668661220775430021065998336/263,-444304085204699509191739392/263,-24659288086654976596721664/263]$ |
$y^2 + x^2y = x^5 + 38x^4 + 380x^3 + 272x^2 + 56x + 2$ |
| 154936.a.309872.1 |
154936.a |
\( 2^{3} \cdot 107 \cdot 181 \) |
\( - 2^{4} \cdot 107 \cdot 181 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.782428\) |
\(3.520926\) |
$[2336,21280528,-43686028900,-1239488]$ |
$[1168,-3489912,6008416516,-1290413819264,-309872]$ |
$[-135860819918848/19367,3248173688832/181,-512301625820224/19367]$ |
$y^2 + (x + 1)y = 2x^5 - 28x^3 - 54x^2 - 52x - 49$ |
| 179496.a.358992.1 |
179496.a |
\( 2^{3} \cdot 3^{4} \cdot 277 \) |
\( - 2^{4} \cdot 3^{4} \cdot 277 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(1.000000\) |
\(0.598914\) |
\(2.695113\) |
$[17376,70133040,154951887708,-1435968]$ |
$[8688,-8543784,12510204484,8923102879584,-358992]$ |
$[-38193904661495808/277,4323193709221888/277,-6557548945605184/2493]$ |
$y^2 + xy = 2x^5 - 16x^4 + 6x^3 + 24x^2 - 26x - 27$ |
| 195337.c.195337.1 |
195337.c |
\( 229 \cdot 853 \) |
\( 229 \cdot 853 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.907580\) |
\(2.042054\) |
$[129524,916698889,30333180209765,25003136]$ |
$[32381,5492928,859896128,-581990373104,195337]$ |
$[35600105352914711125901/195337,186498213659100224448/195337,901626165638988608/195337]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 31x^4 + 18x^3 + 29x^2 - 13x - 7$ |
| 235237.b.235237.1 |
235237.b |
\( 67 \cdot 3511 \) |
\( 67 \cdot 3511 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.319961\) |
\(2.879653\) |
$[31136,57928528,454137546080,940948]$ |
$[15568,443688,25753696,51018624496,235237]$ |
$[914458739061390573568/235237,1674079783096713216/235237,6241733340258304/235237]$ |
$y^2 + y = x^5 - 15x^4 + 22x^3 + 25x^2 - 28x - 22$ |
| 258357.a.258357.1 |
258357.a |
\( 3 \cdot 11 \cdot 7829 \) |
\( 3 \cdot 11 \cdot 7829 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(1.766348\) |
\(3.974284\) |
$[24752,15988612,110693925423,1033428]$ |
$[12376,3717122,1249461841,411585945333,258357]$ |
$[290336410647019749376/258357,7046082395391183872/258357,191374292674417216/258357]$ |
$y^2 + x^2y = x^5 - 22x^4 - 30x^3 + x^2 + 11x + 2$ |
| 276124.a.276124.1 |
276124.a |
\( 2^{2} \cdot 69031 \) |
\( 2^{2} \cdot 69031 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(8.285631\) |
\(2.982827\) |
$[5452,1908337,2589684039,-35343872]$ |
$[1363,-2107,-1501,-1621328,-276124]$ |
$[-4704129610983043/276124,5335217182729/276124,2788511269/276124]$ |
$y^2 + (x^3 + x^2 + x)y = 3x^4 + 3x^3 + 12x^2 - x$ |
| 279259.a.279259.1 |
279259.a |
\( 17 \cdot 16427 \) |
\( - 17 \cdot 16427 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(7.247795\) |
\(2.609206\) |
$[6272,-164576,-183316832,-1117036]$ |
$[3136,437200,67865696,5420745664,-279259]$ |
$[-303305489096114176/279259,-13483676218163200/279259,-667424915849216/279259]$ |
$y^2 + y = x^5 + 9x^4 + 30x^3 + 28x^2 + 5x$ |
| 320137.a.320137.1 |
320137.a |
\( 23 \cdot 31 \cdot 449 \) |
\( 23 \cdot 31 \cdot 449 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(6.581002\) |
\(3.701814\) |
$[2468,332377,210129005,40977536]$ |
$[617,2013,-1171,-1193669,320137]$ |
$[89418178782857/320137,472823732469/320137,-445786819/320137]$ |
$y^2 + (x^2 + x)y = x^5 - 3x^4 - 9x^3 - 4x^2 + x$ |
| 335164.a.335164.1 |
335164.a |
\( 2^{2} \cdot 83791 \) |
\( 2^{2} \cdot 83791 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(8.229520\) |
\(2.962627\) |
$[5780,-1157135,-1608695847,42900992]$ |
$[1445,135215,9974701,-967413320,335164]$ |
$[6299980938903125/335164,407970174041875/335164,20827425055525/335164]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^4 + 2x^3 - 16x^2 + 9x + 1$ |
| 337355.a.337355.1 |
337355.a |
\( 5 \cdot 109 \cdot 619 \) |
\( - 5 \cdot 109 \cdot 619 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(9.662661\) |
\(3.478558\) |
$[2176,-284576,-202972800,-1349420]$ |
$[1088,96752,11199616,706058176,-337355]$ |
$[-1524559844999168/337355,-124608204242944/337355,-13257478242304/337355]$ |
$y^2 + y = x^5 - x^4 + 10x^3 - 16x^2 + 5x + 1$ |
| 342871.b.342871.1 |
342871.b |
\( 342871 \) |
\( -342871 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.407072\) |
\(3.663649\) |
$[148084,1415381689,52115503116749,-43887488]$ |
$[37021,-1867802,93761116,-4388508942,-342871]$ |
$[-69540967411549073069101/342871,94770958473167416322/342871,-128504713926916156/342871]$ |
$y^2 + (x^2 + x + 1)y = -x^6 - 10x^5 - 23x^4 + 34x^3 + 19x^2 - 15x - 7$ |
| 350464.a.350464.1 |
350464.a |
\( 2^{8} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(6.632969\) |
\(3.731045\) |
$[302,5032,388574,1369]$ |
$[604,1782,-1772,-1061453,350464]$ |
$[314010903004/1369,3067669341/2738,-10100843/5476]$ |
$y^2 = x^5 - 3x^4 - 11x^3 - 8x^2 - x$ |
| 354069.a.354069.1 |
354069.a |
\( 3^{2} \cdot 39341 \) |
\( 3^{2} \cdot 39341 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(7.861199\) |
\(2.830032\) |
$[3424,718960,617385920,-1416276]$ |
$[1712,2296,1024,-879632,-354069]$ |
$[-14706820835704832/354069,-11520813989888/354069,-3001286656/354069]$ |
$y^2 + y = x^5 + 16x^4 + 8x^3 + 5x^2 + x$ |
| 356211.b.356211.1 |
356211.b |
\( 3^{3} \cdot 79 \cdot 167 \) |
\( - 3^{3} \cdot 79 \cdot 167 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.488361\) |
\(4.395250\) |
$[47544,170813520,1962824156424,-1424844]$ |
$[23772,-4922754,994832028,-146089993725,-356211]$ |
$[-281167321565803631616/13193,2449297472511636096/13193,-20821760065248576/13193]$ |
$y^2 + y = x^5 - 52x^4 + 57x^3 - 9x^2 - 3x - 1$ |
| 362107.a.362107.1 |
362107.a |
\( 362107 \) |
\( -362107 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.720122\) |
\(6.481098\) |
$[20888,36129472,179160940408,-1448428]$ |
$[10444,-1476698,199538380,-24164535621,-362107]$ |
$[-124260848769120308224/362107,1682256736697436032/362107,-21765075012479680/362107]$ |
$y^2 + y = x^5 - 43x^4 - 75x^3 - 41x^2 - 8x - 1$ |
| 444277.a.444277.1 |
444277.a |
\( 19 \cdot 67 \cdot 349 \) |
\( 19 \cdot 67 \cdot 349 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(2.028807\) |
\(4.564816\) |
$[86848,36102472,1108181907559,1777108]$ |
$[43424,72551412,138990135761,192950068022980,444277]$ |
$[154400651987390377754624/444277,5940668888780495781888/444277,262085884423124673536/444277]$ |
$y^2 + x^2y = x^5 - 13x^4 + 28x^3 + 82x^2 + 7x - 34$ |
| 449957.d.449957.1 |
449957.d |
\( 37 \cdot 12161 \) |
\( 37 \cdot 12161 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(15.840243\) |
\(2.227534\) |
$[11456,8132488,23324821735,1799828]$ |
$[5728,11668,4561,-27504204,449957]$ |
$[6166163646859706368/449957,2192832444891136/449957,149646337024/449957]$ |
$y^2 + xy = x^5 + 20x^4 + 42x^3 + 24x^2 + x$ |
| 461180.a.461180.1 |
461180.a |
\( 2^{2} \cdot 5 \cdot 23059 \) |
\( 2^{2} \cdot 5 \cdot 23059 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(7.543729\) |
\(2.715742\) |
$[8268,4226481,8752341735,-59031040]$ |
$[2067,1917,-4941,-3471984,-461180]$ |
$[-37731353381335107/461180,-16929477040671/461180,21110368149/461180]$ |
$y^2 + (x^3 + 1)y = 3x^4 + 3x^3 + 9x^2 + 20x + 11$ |
| 484013.a.484013.1 |
484013.a |
\( 431 \cdot 1123 \) |
\( 431 \cdot 1123 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.655451\) |
\(5.899063\) |
$[8120,3288688,6910199672,1936052]$ |
$[4060,138702,5266892,536334179,484013]$ |
$[1103138819977600000/484013,9282411646032000/484013,86817340971200/484013]$ |
$y^2 + y = x^5 - 3x^4 - 15x^3 + 17x - 7$ |
| 493528.a.987056.1 |
493528.a |
\( 2^{3} \cdot 7^{2} \cdot 1259 \) |
\( 2^{4} \cdot 7^{2} \cdot 1259 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$9$ |
\( 2 \) |
\(0.308357\) |
\(0.671858\) |
\(3.729100\) |
$[265464,4876857948,318019086615348,-3948224]$ |
$[132732,-78735332,45902102012,-26643675223360,-987056]$ |
$[-2574887205210133239433152/61691,11507383731692448218736/61691,-50543331894663215868/61691]$ |
$y^2 + xy = 2x^5 - 27x^4 + 15x^3 - 162x^2 + 27x - 242$ |
| 495324.a.495324.1 |
495324.a |
\( 2^{2} \cdot 3^{2} \cdot 13759 \) |
\( 2^{2} \cdot 3^{2} \cdot 13759 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(4.812843\) |
\(1.732624\) |
$[36532,7280305,107920170905,63401472]$ |
$[9133,3172141,1034104301,-154500985712,495324]$ |
$[63542937568118240893/495324,2416533700933308817/495324,86256386348574389/495324]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 12x^4 + 45x^3 + 38x^2 - 7x$ |
| 537289.a.537289.1 |
537289.a |
\( 733^{2} \) |
\( 733^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(5.934576\) |
\(3.338199\) |
$[2980,502105,380797165,68772992]$ |
$[745,2205,-2195,-1624325,537289]$ |
$[229499299215625/537289,911753443125/537289,-1218279875/537289]$ |
$y^2 + (x^2 + x)y = x^5 - 9x^4 + 12x^3 - 4x^2 - x$ |
| 543321.a.543321.1 |
543321.a |
\( 3^{3} \cdot 20123 \) |
\( 3^{3} \cdot 20123 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(1.000978\) |
\(9.008805\) |
$[3468,2319129,4044391587,-69545088]$ |
$[867,-65310,-31391692,-7870498266,-543321]$ |
$[-18143945104041/20123,1576424631390/20123,2621865507532/60369]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 8x^4 - 3x^3 - 6x^2 + 4x - 1$ |
| 574220.a.574220.1 |
574220.a |
\( 2^{2} \cdot 5 \cdot 28711 \) |
\( - 2^{2} \cdot 5 \cdot 28711 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.531679\) |
\(4.785107\) |
$[89932,486172177,18152506043415,73500160]$ |
$[22483,804713,-99298993589,-558296708968464,574220]$ |
$[5744752229981082192643/574220,9145423025841542531/574220,-50194180471744812221/574220]$ |
$y^2 + (x^2 + x + 1)y = -x^6 + 4x^4 - 22x^3 - 2x^2 + 76x - 59$ |
| 662773.a.662773.1 |
662773.a |
\( 662773 \) |
\( 662773 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(7.216231\) |
\(2.597843\) |
$[5120,1627120,2085271344,-2651092]$ |
$[2560,1880,-16816,-11645840,-662773]$ |
$[-109951162777600000/662773,-31541166080000/662773,110205337600/662773]$ |
$y^2 + y = x^5 + 25x^4 - 20x^3 + 9x^2 - 2x$ |
| 754714.a.754714.1 |
754714.a |
\( 2 \cdot 353 \cdot 1069 \) |
\( 2 \cdot 353 \cdot 1069 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(4.059645\) |
\(2.283550\) |
$[2412932,1567585,1298608484465,96603392]$ |
$[603233,15162020196,508119037862396,19156828785733711963,754714]$ |
$[79877682924445455585045671393/754714,1664111225481192944720503026/377357,92449731628391825613412222/377357]$ |
$y^2 + (x^2 + x)y = x^5 - 30x^4 + 219x^3 + 26x^2 + x$ |
| 779665.a.779665.1 |
779665.a |
\( 5 \cdot 19 \cdot 29 \cdot 283 \) |
\( 5 \cdot 19 \cdot 29 \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(1.572211\) |
\(3.537474\) |
$[73576,72542248,1931525717459,3118660]$ |
$[36788,44299498,24184595385,-268185657007156,779665]$ |
$[67379981757512627975168/779665,2205552186612911152256/779665,225726828290483472/5377]$ |
$y^2 + xy = x^5 - 17x^4 + 81x^3 - 60x^2 - 118x - 33$ |
| 820897.b.820897.1 |
820897.b |
\( 7^{2} \cdot 11 \cdot 1523 \) |
\( 7^{2} \cdot 11 \cdot 1523 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(9.422560\) |
\(2.355640\) |
$[22388,8145649,65986150361,105074816]$ |
$[5597,965865,17067121,-209342630497,820897]$ |
$[5492581812975067757/820897,169348888115109645/820897,534651612898489/820897]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 9x^4 - 4x^3 + 20x^2 - 5x$ |
| 853157.a.853157.1 |
853157.a |
\( 19 \cdot 83 \cdot 541 \) |
\( 19 \cdot 83 \cdot 541 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(1.118218\) |
\(2.515991\) |
$[157264,100676224,4955817365591,3412628]$ |
$[78632,240845272,941271307905,4001900109607994,853157]$ |
$[3006052840066019496722432/853157,117094390767195242295296/853157,5819872424433878406720/853157]$ |
$y^2 + x^2y = x^5 + 16x^4 + 56x^3 - 87x^2 - 53x - 7$ |
| 858491.a.858491.1 |
858491.a |
\( 409 \cdot 2099 \) |
\( - 409 \cdot 2099 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(5.049863\) |
\(1.817951\) |
$[17584,547708,5545501647,-3433964]$ |
$[8792,3129518,1179953761,145067638597,-858491]$ |
$[-52533749281767391232/858491,-2126867779553219584/858491,-91209557279331904/858491]$ |
$y^2 + (x^2 + 1)y = x^5 - 8x^4 + 13x^3 + 83x - 212$ |
| 931349.a.931349.1 |
931349.a |
\( 661 \cdot 1409 \) |
\( 661 \cdot 1409 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(0.561685\) |
\(5.055168\) |
$[10496,6099568,16314450407,3725396]$ |
$[5248,130968,3830673,737688720,931349]$ |
$[3980788754670419968/931349,18929828291936256/931349,105502495752192/931349]$ |
$y^2 + x^2y = x^5 - 5x^4 - 18x^3 + 17x - 6$ |
| 967723.a.967723.1 |
967723.a |
\( 41 \cdot 23603 \) |
\( - 41 \cdot 23603 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$9$ |
\( 1 \) |
\(1.000000\) |
\(2.626439\) |
\(5.909488\) |
$[2336,203896,127923335,-3870892]$ |
$[1168,22860,500241,15425472,-967723]$ |
$[-2173773118701568/967723,-36425435627520/967723,-16644897024/23603]$ |
$y^2 + xy = x^5 + 2x^4 - 6x^3 - 13x^2 - x$ |
