| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-\frac{1}{169},\frac{33}{169},\frac{43}{169}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[\frac{4219140959375}{21952},\frac{6203236875}{784},\frac{12905875}{28}]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[108,57,2259,-31872]$ |
$[27,28,32,20,-249]$ |
$[-\frac{4782969}{83},-\frac{183708}{83},-\frac{7776}{83}]$ |
$y^2 + (x^3 + 1)y = x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[\frac{324526850403}{83},\frac{25281736298}{249},-\frac{4178776252}{747}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,\frac{129623}{4},-\frac{1521}{8}]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.205749\) |
\(0.143137\) |
$[64,352,9552,-1108]$ |
$[32,-16,-464,-3776,-277]$ |
$[-\frac{33554432}{277},\frac{524288}{277},\frac{475136}{277}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-\frac{56394933862400000}{277},\frac{217505333248000}{277},-\frac{824813158400}{277}]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.451533\) |
\(0.148969\) |
$[236,505,18451,37632]$ |
$[59,124,564,4475,294]$ |
$[\frac{714924299}{294},\frac{12733498}{147},\frac{327214}{49}]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[\frac{25353016669288549}{8232},\frac{75211396489919}{588},\frac{49431027484}{7}]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(29.256600\) |
\(0.149268\) |
$[108,-39,20835,37760]$ |
$[27,32,-256,-1984,295]$ |
$[\frac{14348907}{295},\frac{629856}{295},-\frac{186624}{295}]$ |
$y^2 + (x^3 + 1)y = -x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.597073\) |
\(0.149268\) |
$[198804,305807001,18482629056189,-37760]$ |
$[49701,90182600,203402032096,494095763610824,-295]$ |
$[-\frac{303267334973269931148501}{295},-\frac{2214359494206283568520}{59},-\frac{502441543825401014496}{295}]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-\frac{1352659309173012149}{168},\frac{419870026410625699}{168},-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.988484\) |
\(0.165612\) |
$[8,208,1464,-1396]$ |
$[4,-34,-124,-413,-349]$ |
$[-\frac{1024}{349},\frac{2176}{349},\frac{1984}{349}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[\frac{229345007}{353},\frac{6021734}{353},\frac{565504}{353}]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[\frac{28596971960000}{81},\frac{1150492082200}{81},\frac{6677950400}{9}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.970596\) |
\(0.189706\) |
$[344,-3068,-526433,-47916]$ |
$[172,1744,45841,1210779,-11979]$ |
$[-\frac{150536645632}{11979},-\frac{8874253312}{11979},-\frac{1356160144}{11979}]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.794119\) |
\(0.189706\) |
$[11096,25612,88274095,-175692]$ |
$[5548,1278244,392069161,135322995423,-43923]$ |
$[-\frac{5256325630316243968}{43923},-\frac{1804005053317888}{363},-\frac{99735603013264}{363}]$ |
$y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(29.135501\) |
\(0.198201\) |
$[36,1569,-13743,99328]$ |
$[9,-62,356,-160,776]$ |
$[\frac{59049}{776},-\frac{22599}{388},\frac{7209}{194}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[2440,51100,45041351,1556]$ |
$[1220,53500,2084961,-79649395,389]$ |
$[\frac{2702708163200000}{389},\frac{97147868000000}{389},\frac{3103255952400}{389}]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.798620\) |
\(0.197986\) |
$[16,100,1775,1556]$ |
$[8,-14,-159,-367,389]$ |
$[\frac{32768}{389},-\frac{7168}{389},-\frac{10176}{389}]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[80,-20,649,-12608]$ |
$[40,70,39,-835,-3152]$ |
$[-\frac{6400000}{197},-\frac{280000}{197},-\frac{3900}{197}]$ |
$y^2 + (x + 1)y = -x^5$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[\frac{58632501248}{25},\frac{2327987904}{25},4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-\frac{39466820645749}{61},-\frac{1672794336220}{61},-\frac{96756008472}{61}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(31.171156\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[\frac{6080953884912}{7},\frac{155007628668}{7},-1306723104]$ |
$y^2 + (x^3 + x)y = -2x^4 + 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[\frac{6080953884912}{7},\frac{155007628668}{7},-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[\frac{6240321451}{2700},\frac{8289281}{150},0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[23444,212089,1627179821,4665600]$ |
$[5861,1422468,457836300,164990835819,36450]$ |
$[\frac{6916057684302385301}{36450},\frac{5303516319500302}{675},\frac{1294426477922}{3}]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.048435\) |
\(0.245886\) |
$[1176,144,66456,1844]$ |
$[588,14382,467132,16957923,461]$ |
$[\frac{70288881159168}{461},\frac{2923824242304}{461},\frac{161508086208}{461}]$ |
$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.245886\) |
\(0.245886\) |
$[80664,166117104,3752725952952,1844]$ |
$[40332,40091742,45075737276,52661714805267,461]$ |
$[\frac{106720731303787612818432}{461},\frac{2630293443843585469056}{461},\frac{73323359651716069824}{461}]$ |
$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[136,280,15060,1856]$ |
$[68,146,-64,-6417,464]$ |
$[\frac{90870848}{29},\frac{2869192}{29},-\frac{18496}{29}]$ |
$y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[680,-5255,-1253953,-3712]$ |
$[680,22770,1180736,71106895,-29696]$ |
$[-\frac{141985700000}{29},-\frac{6991813125}{29},-\frac{533176100}{29}]$ |
$y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.802679\) |
\(0.225335\) |
$[45368,202225,3012190355,-3712]$ |
$[45368,85625826,215176422416,607585463496703,-29696]$ |
$[-\frac{187693059992988715232}{29},-\frac{7808250185554819143}{29},-\frac{432507850151022641}{29}]$ |
$y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(29.113273\) |
\(0.227447\) |
$[280,760,60604,-3776]$ |
$[140,690,4544,40015,-944]$ |
$[-\frac{3361400000}{59},-\frac{118335000}{59},-\frac{5566400}{59}]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.278318\) |
\(0.227447\) |
$[152,17065,1592025,7552]$ |
$[152,-10414,-926656,-62325777,60416]$ |
$[\frac{79235168}{59},-\frac{35714813}{59},-\frac{20907676}{59}]$ |
$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(26.722339\) |
\(0.247429\) |
$[7340,1042345,2905273355,121856]$ |
$[1835,96870,-3910340,-4139817700,952]$ |
$[\frac{20805604708146875}{952},\frac{299272981175625}{476},-\frac{27661753375}{2}]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[\frac{13181630464}{121},\frac{49057344}{11},\frac{31824640}{121}]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.782699\) |
\(0.243209\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[\frac{12063042849801664}{243},\frac{167186257609000}{81},\frac{3083035208512}{27}]$ |
$y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.819904\) |
\(0.248199\) |
$[120,-540,-29169,-2092]$ |
$[60,240,2241,19215,-523]$ |
$[-\frac{777600000}{523},-\frac{51840000}{523},-\frac{8067600}{523}]$ |
$y^2 + (x + 1)y = x^5 - x^4 - x^3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-\frac{126810465636208320000000000}{523},-\frac{5276053055713522320000000}{523},-\frac{292288477352026798440000}{523}]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.060256\) |
\(0.248432\) |
$[284,2401,246639,-67712]$ |
$[71,110,-624,-14101,-529]$ |
$[-\frac{1804229351}{529},-\frac{39370210}{529},\frac{3145584}{529}]$ |
$y^2 + (x^3 + x + 1)y = -x^5$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.692472\) |
\(0.256925\) |
$[1264,18124,6869487,33300]$ |
$[632,13622,351361,9125317,8325]$ |
$[\frac{100828984082432}{8325},\frac{3438682756096}{8325},\frac{140342016064}{8325}]$ |
$y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(11.546350\) |
\(0.288659\) |
$[68,-55823,-955895,-37617664]$ |
$[17,2338,2304,-1356769,-293888]$ |
$[-\frac{1419857}{293888},-\frac{820471}{20992},-\frac{2601}{1148}]$ |
$y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[\frac{22717712}{9},\frac{540430}{9},-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[\frac{5071050752}{9},\frac{195344320}{9},1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.910299\) |
\(0.289798\) |
$[228,705,135777,295936]$ |
$[57,106,-992,-16945,2312]$ |
$[\frac{601692057}{2312},\frac{9815229}{1156},-\frac{402876}{289}]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$ |
| 587.a.587.1 |
587.a |
\( 587 \) |
\( 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.003773\) |
\(29.510964\) |
\(0.111352\) |
$[60,1401,54147,-75136]$ |
$[15,-49,-501,-2479,-587]$ |
$[-\frac{759375}{587},\frac{165375}{587},\frac{112725}{587}]$ |
$y^2 + (x^3 + x + 1)y = -x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(20.658150\) |
\(0.286919\) |
$[748,11545,2902787,2408448]$ |
$[187,976,-192,-247120,18816]$ |
$[\frac{228669389707}{18816},\frac{398891383}{1176},-\frac{34969}{98}]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.411617\) |
\(0.294115\) |
$[120,192,9912,2388]$ |
$[60,118,-68,-4501,597]$ |
$[\frac{259200000}{199},\frac{8496000}{199},-\frac{81600}{199}]$ |
$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$ |
