| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[\frac{324526850403}{83},\frac{25281736298}{249},-\frac{4178776252}{747}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.578417\) |
\(0.143137\) |
$[4480,1370512,1511819744,-1108]$ |
$[2240,-19352,164384,-1569936,-277]$ |
$[-\frac{56394933862400000}{277},\frac{217505333248000}{277},-\frac{824813158400}{277}]$ |
$y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.597073\) |
\(0.149268\) |
$[198804,305807001,18482629056189,-37760]$ |
$[49701,90182600,203402032096,494095763610824,-295]$ |
$[-\frac{303267334973269931148501}{295},-\frac{2214359494206283568520}{59},-\frac{502441543825401014496}{295}]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.495495\) |
\(0.185913\) |
$[188,817,30871,45184]$ |
$[47,58,256,2167,353]$ |
$[\frac{229345007}{353},\frac{6021734}{353},\frac{565504}{353}]$ |
$y^2 + (x^3 + x + 1)y = x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-\frac{39466820645749}{61},-\frac{1672794336220}{61},-\frac{96756008472}{61}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.278318\) |
\(0.227447\) |
$[152,17065,1592025,7552]$ |
$[152,-10414,-926656,-62325777,60416]$ |
$[\frac{79235168}{59},-\frac{35714813}{59},-\frac{20907676}{59}]$ |
$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-\frac{126810465636208320000000000}{523},-\frac{5276053055713522320000000}{523},-\frac{292288477352026798440000}{523}]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 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.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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[\frac{5071050752}{9},\frac{195344320}{9},1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 587.a.587.1 |
587.a |
\( 587 \) |
\( 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.003773\) |
\(29.510964\) |
\(0.111352\) |
$[60,1401,54147,-75136]$ |
$[15,-49,-501,-2479,-587]$ |
$[-\frac{759375}{587},\frac{165375}{587},\frac{112725}{587}]$ |
$y^2 + (x^3 + x + 1)y = -x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.411617\) |
\(0.294115\) |
$[120,192,9912,2388]$ |
$[60,118,-68,-4501,597]$ |
$[\frac{259200000}{199},\frac{8496000}{199},-\frac{81600}{199}]$ |
$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[1672,75628,49887881,2412]$ |
$[836,16516,-1263521,-332270453,603]$ |
$[\frac{408348897330176}{603},\frac{9649919856896}{603},-\frac{883069772816}{603}]$ |
$y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(26.910016\) |
\(0.269100\) |
$[176,148,7375,-2412]$ |
$[88,298,1361,7741,-603]$ |
$[-\frac{5277319168}{603},-\frac{203078656}{603},-\frac{10539584}{603}]$ |
$y^2 + (x^2 + 1)y = x^5 - x^3 + x$ |
| 604.a.9664.1 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.291788\) |
\(0.291788\) |
$[49556,-797087975,-23996873337603,1236992]$ |
$[12389,39607304,223396249616,299729401586052,9664]$ |
$[\frac{291864493641401980949}{9664},\frac{9414430497536890397}{1208},\frac{2143030742187944921}{604}]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$ |
| 604.a.9664.2 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\Z/27\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(23.634831\) |
\(0.291788\) |
$[116,6265,95277,1236992]$ |
$[29,-226,836,-6708,9664]$ |
$[\frac{20511149}{9664},-\frac{2755957}{4832},\frac{175769}{2416}]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$ |
| 644.b.14812.1 |
644.b |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{2} \cdot 7 \cdot 23^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.435107\) |
\(0.308702\) |
$[1268,-40511,-17688719,-1895936]$ |
$[317,5875,170781,4905488,-14812]$ |
$[-\frac{3201078401357}{14812},-\frac{187148201375}{14812},-\frac{17161611909}{14812}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$ |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[\frac{2909390022551}{17576},\frac{4602275343}{676},\frac{10349147}{26}]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 688.a.2752.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{6} \cdot 43 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(25.707298\) |
\(0.321341\) |
$[32,112,-680,-344]$ |
$[32,-32,1344,10496,-2752]$ |
$[-\frac{524288}{43},\frac{16384}{43},-\frac{21504}{43}]$ |
$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$ |
| 688.a.704512.2 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{14} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.426825\) |
\(0.321341\) |
$[464,-248,-39602,-86]$ |
$[1856,146176,15688704,1937702912,-704512]$ |
$[-\frac{1344218660864}{43},-\frac{57041383424}{43},-\frac{3298550016}{43}]$ |
$y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$ |
| 688.a.704512.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( 2^{14} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(6.426825\) |
\(0.321341\) |
$[128,532,26830,86]$ |
$[512,5248,-408576,-59183104,704512]$ |
$[\frac{2147483648}{43},\frac{42991616}{43},-\frac{6537216}{43}]$ |
$y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.812569\) |
\(0.293946\) |
$[104,-824,-20333,-2764]$ |
$[52,250,601,-7812,-691]$ |
$[-\frac{380204032}{691},-\frac{35152000}{691},-\frac{1625104}{691}]$ |
$y^2 + (x + 1)y = x^5 - x^3 - x^2$ |
| 704.a.45056.1 |
704.a |
\( 2^{6} \cdot 11 \) |
\( - 2^{12} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.976027\) |
\(0.332667\) |
$[134,-464,-15328,-176]$ |
$[268,4230,61444,-356477,-45056]$ |
$[-\frac{1350125107}{44},-\frac{636113745}{352},-\frac{68955529}{704}]$ |
$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$ |
| 708.a.2832.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( 2^{4} \cdot 3 \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[148,2065,76361,362496]$ |
$[37,-29,-59,-756,2832]$ |
$[\frac{69343957}{2832},-\frac{1468937}{2832},-\frac{1369}{48}]$ |
$y^2 + (x^2 + x + 1)y = x^5$ |
| 708.a.19116.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{2} \cdot 3^{4} \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[908,-132815,8426215,2446848]$ |
$[227,7681,-438901,-39657072,19116]$ |
$[\frac{602738989907}{19116},\frac{89845294523}{19116},-\frac{383324231}{324}]$ |
$y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$ |
| 708.a.181248.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{10} \cdot 3 \cdot 59 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.325344\) |
\(0.325344\) |
$[234100,3468879025,202585466081177,-23199744]$ |
$[58525,-1820975,60952909,62829762150,-181248]$ |
$[-\frac{686605237334059580078125}{181248},\frac{365029741228054296875}{181248},-\frac{208774418179643125}{181248}]$ |
$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.361162\) |
\(0.286893\) |
$[160,-1280,-42089,2836]$ |
$[80,480,1121,-35180,709]$ |
$[\frac{3276800000}{709},\frac{245760000}{709},\frac{7174400}{709}]$ |
$y^2 + xy = x^5 - 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004592\) |
\(27.957889\) |
\(0.128395\) |
$[36,1305,-2547,91264]$ |
$[9,-51,173,-261,713]$ |
$[\frac{59049}{713},-\frac{37179}{713},\frac{14013}{713}]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.149881\) |
\(0.285801\) |
$[92,73,6379,-91264]$ |
$[23,19,-41,-326,-713]$ |
$[-\frac{279841}{31},-\frac{10051}{31},\frac{943}{31}]$ |
$y^2 + (x^3 + x + 1)y = -x^4$ |
| 731.a.12427.1 |
731.a |
\( 17 \cdot 43 \) |
\( - 17^{2} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.926779\) |
\(0.298536\) |
$[480,-21564,-3373785,-49708]$ |
$[240,5994,167265,1053891,-12427]$ |
$[-\frac{796262400000}{12427},-\frac{82861056000}{12427},-\frac{9634464000}{12427}]$ |
$y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$ |
| 741.a.28899.1 |
741.a |
\( 3 \cdot 13 \cdot 19 \) |
\( - 3^{2} \cdot 13^{2} \cdot 19 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.756843\) |
\(0.293076\) |
$[576,-840,740385,115596]$ |
$[288,3596,-38169,-5980972,28899]$ |
$[\frac{220150628352}{3211},\frac{9544531968}{3211},-\frac{351765504}{3211}]$ |
$y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$ |
| 743.a.743.1 |
743.a |
\( 743 \) |
\( -743 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004577\) |
\(28.765391\) |
\(0.131656\) |
$[28,1945,15219,95104]$ |
$[7,-79,-53,-1653,743]$ |
$[\frac{16807}{743},-\frac{27097}{743},-\frac{2597}{743}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2$ |
