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 |
169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
196.a.21952.1 |
196.a |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/6\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.360.3, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[4219140959375/21952,6203236875/784,12905875/28]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
249.a.249.1 |
249.a |
\( 3 \cdot 83 \) |
\( 3 \cdot 83 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[108,57,2259,-31872]$ |
$[27,28,32,20,-249]$ |
$[-4782969/83,-183708/83,-7776/83]$ |
$y^2 + (x^3 + 1)y = x^2 + x$ |
249.a.6723.1 |
249.a |
\( 3 \cdot 83 \) |
\( - 3^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/28\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[324526850403/83,25281736298/249,-4178776252/747]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
277.a.277.1 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.205749\) |
\(0.143137\) |
$[64,352,9552,-1108]$ |
$[32,-16,-464,-3776,-277]$ |
$[-33554432/277,524288/277,475136/277]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$ |
277.a.277.2 |
277.a |
\( 277 \) |
\( 277 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-56394933862400000/277,217505333248000/277,-824813158400/277]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
294.a.294.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( - 2 \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.451533\) |
\(0.148969\) |
$[236,505,18451,37632]$ |
$[59,124,564,4475,294]$ |
$[714924299/294,12733498/147,327214/49]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2$ |
294.a.8232.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{3} \cdot 3 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[25353016669288549/8232,75211396489919/588,49431027484/7]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
295.a.295.1 |
295.a |
\( 5 \cdot 59 \) |
\( - 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(29.256600\) |
\(0.149268\) |
$[108,-39,20835,37760]$ |
$[27,32,-256,-1984,295]$ |
$[14348907/295,629856/295,-186624/295]$ |
$y^2 + (x^3 + 1)y = -x^2$ |
295.a.295.2 |
295.a |
\( 5 \cdot 59 \) |
\( - 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.597073\) |
\(0.149268\) |
$[198804,305807001,18482629056189,-37760]$ |
$[49701,90182600,203402032096,494095763610824,-295]$ |
$[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$ |
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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
336.a.172032.1 |
336.a |
\( 2^{4} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
349.a.349.1 |
349.a |
\( 349 \) |
\( 349 \) |
$0$ |
$0$ |
$\Z/13\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.988484\) |
\(0.165612\) |
$[8,208,1464,-1396]$ |
$[4,-34,-124,-413,-349]$ |
$[-1024/349,2176/349,1984/349]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$ |
353.a.353.1 |
353.a |
\( 353 \) |
\( -353 \) |
$0$ |
$0$ |
$\Z/11\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[229345007/353,6021734/353,565504/353]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
360.a.6480.1 |
360.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
363.a.11979.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3^{2} \cdot 11^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.970596\) |
\(0.189706\) |
$[344,-3068,-526433,-47916]$ |
$[172,1744,45841,1210779,-11979]$ |
$[-150536645632/11979,-8874253312/11979,-1356160144/11979]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$ |
363.a.43923.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3 \cdot 11^{4} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.794119\) |
\(0.189706\) |
$[11096,25612,88274095,-175692]$ |
$[5548,1278244,392069161,135322995423,-43923]$ |
$[-5256325630316243968/43923,-1804005053317888/363,-99735603013264/363]$ |
$y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$ |
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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(29.135501\) |
\(0.198201\) |
$[36,1569,-13743,99328]$ |
$[9,-62,356,-160,776]$ |
$[59049/776,-22599/388,7209/194]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$ |
389.a.389.1 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[2440,51100,45041351,1556]$ |
$[1220,53500,2084961,-79649395,389]$ |
$[2702708163200000/389,97147868000000/389,3103255952400/389]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$ |
389.a.389.2 |
389.a |
\( 389 \) |
\( 389 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[16,100,1775,1556]$ |
$[8,-14,-159,-367,389]$ |
$[32768/389,-7168/389,-10176/389]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
394.a.394.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2 \cdot 197 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[11032,106300,393913607,1576]$ |
$[5516,1250044,371875905,122164372511,394]$ |
$[12960598758485504,532478222573696,28717744887720]$ |
$y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9$ |
394.a.3152.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2^{4} \cdot 197 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[80,-20,649,-12608]$ |
$[40,70,39,-835,-3152]$ |
$[-6400000/197,-280000/197,-3900/197]$ |
$y^2 + (x + 1)y = -x^5$ |
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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
427.a.2989.1 |
427.a |
\( 7 \cdot 61 \) |
\( - 7^{2} \cdot 61 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-39466820645749/61,-1672794336220/61,-96756008472/61]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
448.a.448.2 |
448.a |
\( 2^{6} \cdot 7 \) |
\( - 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
448.a.448.1 |
448.a |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
450.a.2700.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[6240321451/2700,8289281/150,0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
450.a.36450.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[23444,212089,1627179821,4665600]$ |
$[5861,1422468,457836300,164990835819,36450]$ |
$[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$ |
461.a.461.1 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.048435\) |
\(0.245886\) |
$[1176,144,66456,1844]$ |
$[588,14382,467132,16957923,461]$ |
$[70288881159168/461,2923824242304/461,161508086208/461]$ |
$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$ |
461.a.461.2 |
461.a |
\( 461 \) |
\( 461 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.245886\) |
\(0.245886\) |
$[80664,166117104,3752725952952,1844]$ |
$[40332,40091742,45075737276,52661714805267,461]$ |
$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$ |
$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$ |
464.a.464.1 |
464.a |
\( 2^{4} \cdot 29 \) |
\( 2^{4} \cdot 29 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[136,280,15060,1856]$ |
$[68,146,-64,-6417,464]$ |
$[90870848/29,2869192/29,-18496/29]$ |
$y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$ |
464.a.29696.1 |
464.a |
\( 2^{4} \cdot 29 \) |
\( - 2^{10} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[680,-5255,-1253953,-3712]$ |
$[680,22770,1180736,71106895,-29696]$ |
$[-141985700000/29,-6991813125/29,-533176100/29]$ |
$y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$ |
464.a.29696.2 |
464.a |
\( 2^{4} \cdot 29 \) |
\( - 2^{10} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.802679\) |
\(0.225335\) |
$[45368,202225,3012190355,-3712]$ |
$[45368,85625826,215176422416,607585463496703,-29696]$ |
$[-187693059992988715232/29,-7808250185554819143/29,-432507850151022641/29]$ |
$y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$ |
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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(29.113273\) |
\(0.227447\) |
$[280,760,60604,-3776]$ |
$[140,690,4544,40015,-944]$ |
$[-3361400000/59,-118335000/59,-5566400/59]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$ |
472.a.60416.1 |
472.a |
\( 2^{3} \cdot 59 \) |
\( 2^{10} \cdot 59 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.278318\) |
\(0.227447\) |
$[152,17065,1592025,7552]$ |
$[152,-10414,-926656,-62325777,60416]$ |
$[79235168/59,-35714813/59,-20907676/59]$ |
$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$ |
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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[20805604708146875/952,299272981175625/476,-27661753375/2]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
484.a.1936.1 |
484.a |
\( 2^{2} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[13181630464/121,49057344/11,31824640/121]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |