| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.245886\) |
\(0.245886\) |
$[80664,166117104,3752725952952,1844]$ |
$[40332,40091742,45075737276,52661714805267,461]$ |
$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$ |
$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$ |
| 587.a.587.1 |
587.a |
\( 587 \) |
\( 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.003773\) |
\(29.510964\) |
\(0.111352\) |
$[60,1401,54147,-75136]$ |
$[15,-49,-501,-2479,-587]$ |
$[-759375/587,165375/587,112725/587]$ |
$y^2 + (x^3 + x + 1)y = -x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.291788\) |
\(0.291788\) |
$[49556,-797087975,-23996873337603,1236992]$ |
$[12389,39607304,223396249616,299729401586052,9664]$ |
$[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004592\) |
\(27.957889\) |
\(0.128395\) |
$[36,1305,-2547,91264]$ |
$[9,-51,173,-261,713]$ |
$[59049/713,-37179/713,14013/713]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x$ |
| 743.a.743.1 |
743.a |
\( 743 \) |
\( -743 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004577\) |
\(28.765391\) |
\(0.131656\) |
$[28,1945,15219,95104]$ |
$[7,-79,-53,-1653,743]$ |
$[16807/743,-27097/743,-2597/743]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2$ |
| 893.a.893.1 |
893.a |
\( 19 \cdot 47 \) |
\( 19 \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006429\) |
\(23.402435\) |
\(0.150459\) |
$[156,-519,-11805,-114304]$ |
$[39,85,67,-1153,-893]$ |
$[-90224199/893,-5042115/893,-101907/893]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2$ |
| 932.a.3728.1 |
932.a |
\( 2^{2} \cdot 233 \) |
\( - 2^{4} \cdot 233 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002250\) |
\(25.168364\) |
\(0.169871\) |
$[8,229,527,-466]$ |
$[8,-150,-128,-5881,-3728]$ |
$[-2048/233,4800/233,512/233]$ |
$y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$ |
| 953.a.953.1 |
953.a |
\( 953 \) |
\( -953 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006276\) |
\(24.886682\) |
\(0.156194\) |
$[92,1513,26203,121984]$ |
$[23,-41,67,-35,953]$ |
$[6436343/953,-498847/953,35443/953]$ |
$y^2 + (x^3 + x + 1)y = x^3 + x^2$ |
| 961.a.961.1 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.224644\) |
\(0.449288\) |
$[66980,1011437281,14016353908561,-123008]$ |
$[16745,-30460094,12221475912,-180792178085599,-961]$ |
$[-1316514841399349215625/961,143016680917998700750/961,-3426841043882137800/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$ |
| 971.a.971.1 |
971.a |
\( 971 \) |
\( -971 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.005970\) |
\(29.647111\) |
\(0.176998\) |
$[256,1024,80304,-3884]$ |
$[128,512,2000,-1536,-971]$ |
$[-34359738368/971,-1073741824/971,-32768000/971]$ |
$y^2 + y = x^5 - 2x^3 + x$ |
| 1051.a.1051.1 |
1051.a |
\( 1051 \) |
\( -1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007925\) |
\(23.437821\) |
\(0.185743\) |
$[96,-144,144,4204]$ |
$[48,120,-80,-4560,1051]$ |
$[254803968/1051,13271040/1051,-184320/1051]$ |
$y^2 + y = x^5 - x^4 + x^2 - x$ |
| 1077.b.1077.2 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.406291\) |
\(0.406291\) |
$[107840,22281904,765878465200,4308]$ |
$[53920,117426616,333407026000,1047074174177136,1077]$ |
$[455773864377135923200000/1077,18408406506675601408000/1077,969336384916326400000/1077]$ |
$y^2 + y = x^5 + 14x^4 + 38x^3 - 79x^2 + 15x - 1$ |
| 1083.b.390963.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{4} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.132919\) |
\(0.265837\) |
$[150440,1945515892,68956865081488,-1563852]$ |
$[75220,-88500632,98386538568,-107931608328616,-390963]$ |
$[-2408056349828975363200000/390963,1982406707133537344000/20577,-27053302090985600/19]$ |
$y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$ |
| 1094.a.2188.1 |
1094.a |
\( 2 \cdot 547 \) |
\( 2^{2} \cdot 547 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.003585\) |
\(26.605542\) |
\(0.190768\) |
$[20,3001,-30387,280064]$ |
$[5,-124,596,-3099,2188]$ |
$[3125/2188,-3875/547,3725/547]$ |
$y^2 + (x^3 + 1)y = x^4 - x^2$ |
| 1109.a.1109.1 |
1109.a |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.288506\) |
\(0.288506\) |
$[38880,87301728,855606760992,4436]$ |
$[19440,1196112,510249312,2122140677184,1109]$ |
$[2776395315422822400000/1109,8787404722987008000/1109,192830154395443200/1109]$ |
$y^2 + y = x^5 - 6x^4 - 36x^3 - 6x^2 + 63x - 36$ |
| 1127.a.1127.1 |
1127.a |
\( 7^{2} \cdot 23 \) |
\( - 7^{2} \cdot 23 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.40.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006656\) |
\(25.743921\) |
\(0.171351\) |
$[60,105,37947,144256]$ |
$[15,5,-501,-1885,1127]$ |
$[759375/1127,16875/1127,-112725/1127]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - x$ |
| 1198.a.2396.1 |
1198.a |
\( 2 \cdot 599 \) |
\( 2^{2} \cdot 599 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.004486\) |
\(22.435716\) |
\(0.201311\) |
$[108,729,55683,-306688]$ |
$[27,0,-500,-3375,-2396]$ |
$[-14348907/2396,0,91125/599]$ |
$y^2 + (x^3 + 1)y = -x$ |
| 1205.a.1205.1 |
1205.a |
\( 5 \cdot 241 \) |
\( 5 \cdot 241 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007111\) |
\(29.029132\) |
\(0.206427\) |
$[128,592,16064,4820]$ |
$[64,72,576,7920,1205]$ |
$[1073741824/1205,18874368/1205,2359296/1205]$ |
$y^2 + y = x^5 + 2x^4 - x^2$ |
| 1207.a.1207.1 |
1207.a |
\( 17 \cdot 71 \) |
\( 17 \cdot 71 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008414\) |
\(24.022483\) |
\(0.202128\) |
$[76,889,37395,-154496]$ |
$[19,-22,-308,-1584,-1207]$ |
$[-2476099/1207,150898/1207,111188/1207]$ |
$y^2 + (x^2 + x + 1)y = -x^5 - x^4$ |
| 1253.a.1253.1 |
1253.a |
\( 7 \cdot 179 \) |
\( - 7 \cdot 179 \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.207464\) |
\(0.414928\) |
$[413532,9381037161,999361725629499,160384]$ |
$[103383,54458647,-97243994481,-3254780028624958,1253]$ |
$[1687126365978608485162449/179,8596391751971448839127/179,-829487756384515053]$ |
$y^2 + (x^3 + x^2 + 1)y = -x^6 + 2x^5 - 33x^3 + 43x^2 + 15x - 330$ |
| 1253.b.1253.1 |
1253.b |
\( 7 \cdot 179 \) |
\( - 7 \cdot 179 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009941\) |
\(18.851977\) |
\(0.187411\) |
$[348,2409,250779,160384]$ |
$[87,215,467,-1399,1253]$ |
$[4984209207/1253,141578145/1253,3534723/1253]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^2$ |
| 1269.a.1269.1 |
1269.a |
\( 3^{3} \cdot 47 \) |
\( 3^{3} \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010333\) |
\(20.591707\) |
\(0.212768\) |
$[0,288,1008,-5076]$ |
$[0,-48,112,-576,1269]$ |
$[0,-1048576/6627,-1792/423]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^2 + x$ |
| 1327.a.1327.1 |
1327.a |
\( 1327 \) |
\( 1327 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009412\) |
\(22.632739\) |
\(0.213013\) |
$[52,1321,277,169856]$ |
$[13,-48,200,74,1327]$ |
$[371293/1327,-105456/1327,33800/1327]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 2x^4 + x^3$ |
| 1343.a.1343.1 |
1343.a |
\( 17 \cdot 79 \) |
\( 17 \cdot 79 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007639\) |
\(24.541872\) |
\(0.187477\) |
$[220,649,72811,-171904]$ |
$[55,99,-213,-5379,-1343]$ |
$[-503284375/1343,-16471125/1343,644325/1343]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^4 - x$ |
| 1343.b.1343.1 |
1343.b |
\( 17 \cdot 79 \) |
\( 17 \cdot 79 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013205\) |
\(18.431116\) |
\(0.243377\) |
$[708,-32871,-7418931,171904]$ |
$[177,2675,48537,358856,1343]$ |
$[173726604657/1343,14833498275/1343,1520615673/1343]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 2x^2 + x$ |
| 1383.a.4149.1 |
1383.a |
\( 3 \cdot 461 \) |
\( 3^{2} \cdot 461 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005877\) |
\(19.046404\) |
\(0.223864\) |
$[0,192,3600,-16596]$ |
$[0,-32,400,-256,4149]$ |
$[0,-33554432/17214201,-12800/4149]$ |
$y^2 + y = x^5 + x^4$ |
| 1385.a.6925.1 |
1385.a |
\( 5 \cdot 277 \) |
\( 5^{2} \cdot 277 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006508\) |
\(16.829506\) |
\(0.219038\) |
$[56,-2576,-46840,27700]$ |
$[28,462,1916,-39949,6925]$ |
$[17210368/6925,10141824/6925,1502144/6925]$ |
$y^2 + y = x^5 + 3x^4 + 3x^3 - x$ |
| 1397.a.1397.1 |
1397.a |
\( 11 \cdot 127 \) |
\( 11 \cdot 127 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008804\) |
\(24.985912\) |
\(0.219976\) |
$[24,0,-9000,5588]$ |
$[12,6,1004,3003,1397]$ |
$[248832/1397,10368/1397,144576/1397]$ |
$y^2 + y = x^5 - x^3$ |
| 1403.a.1403.1 |
1403.a |
\( 23 \cdot 61 \) |
\( - 23 \cdot 61 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008805\) |
\(25.036358\) |
\(0.220455\) |
$[88,-32,-7416,-5612]$ |
$[44,86,956,8667,-1403]$ |
$[-164916224/1403,-7325824/1403,-1850816/1403]$ |
$y^2 + y = x^5 + x^4 - x^3 - x^2$ |
| 1468.a.2936.1 |
1468.a |
\( 2^{2} \cdot 367 \) |
\( - 2^{3} \cdot 367 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003870\) |
\(22.107029\) |
\(0.256637\) |
$[220,-719,27031,375808]$ |
$[55,156,-448,-12244,2936]$ |
$[503284375/2936,6488625/734,-169400/367]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x^2$ |
| 1497.a.1497.1 |
1497.a |
\( 3 \cdot 499 \) |
\( 3 \cdot 499 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.021772\) |
\(12.141842\) |
\(0.264354\) |
$[356,2065,274969,191616]$ |
$[89,244,-60,-16219,1497]$ |
$[5584059449/1497,172012436/1497,-158420/499]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - 2x^2 + x - 1$ |
| 1497.b.13473.1 |
1497.b |
\( 3 \cdot 499 \) |
\( 3^{3} \cdot 499 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002757\) |
\(24.920459\) |
\(0.206128\) |
$[92,36025,3650051,-1724544]$ |
$[23,-1479,-41077,-783053,-13473]$ |
$[-6436343/13473,5998331/4491,21729733/13473]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - x^2$ |
| 1499.a.1499.1 |
1499.a |
\( 1499 \) |
\( 1499 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009040\) |
\(25.977263\) |
\(0.234847\) |
$[212,1417,50245,191872]$ |
$[53,58,516,5996,1499]$ |
$[418195493/1499,8634866/1499,1449444/1499]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^2 - x$ |
| 1503.a.4509.1 |
1503.a |
\( 3^{2} \cdot 167 \) |
\( - 3^{3} \cdot 167 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002665\) |
\(25.832365\) |
\(0.206516\) |
$[676,11209,2364277,-577152]$ |
$[169,723,261,-119655,-4509]$ |
$[-137858491849/4509,-1163260969/1503,-828269/501]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 3x^3 + x$ |
| 1519.a.1519.1 |
1519.a |
\( 7^{2} \cdot 31 \) |
\( - 7^{2} \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.40.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011133\) |
\(23.937241\) |
\(0.266486\) |
$[804,1953,517041,-194432]$ |
$[201,1602,16160,170439,-1519]$ |
$[-328080401001/1519,-13009202802/1519,-652880160/1519]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 - x - 1$ |
| 1532.a.392192.1 |
1532.a |
\( 2^{2} \cdot 383 \) |
\( 2^{10} \cdot 383 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.518452\) |
\(0.518452\) |
$[52500,33335793,517241464281,50200576]$ |
$[13125,5788743,3113886477,1840053622644,392192]$ |
$[389490222930908203125/392192,13088268780029296875/392192,536415600139453125/392192]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 7x^4 - 53x^2 + 12x - 1$ |
| 1544.a.3088.1 |
1544.a |
\( 2^{3} \cdot 193 \) |
\( - 2^{4} \cdot 193 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005918\) |
\(20.256903\) |
\(0.239772\) |
$[40,109,589,386]$ |
$[40,-6,432,4311,3088]$ |
$[6400000/193,-24000/193,43200/193]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^2$ |
| 1549.a.1549.1 |
1549.a |
\( 1549 \) |
\( 1549 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011914\) |
\(22.603960\) |
\(0.269299\) |
$[772,673,79825,198272]$ |
$[193,1524,17036,241343,1549]$ |
$[267785184193/1549,10956122868/1549,634573964/1549]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^3 - 3x$ |
| 1612.a.3224.1 |
1612.a |
\( 2^{2} \cdot 13 \cdot 31 \) |
\( 2^{3} \cdot 13 \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004500\) |
\(20.032411\) |
\(0.270409\) |
$[156,609,32271,-412672]$ |
$[39,38,-36,-712,-3224]$ |
$[-6940323/248,-86697/124,1053/62]$ |
$y^2 + (x^3 + x + 1)y = x^3 + 2x^2 + x$ |
| 1637.a.1637.1 |
1637.a |
\( 1637 \) |
\( 1637 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.012103\) |
\(20.489120\) |
\(0.247972\) |
$[40,-800,-7256,-6548]$ |
$[20,150,84,-5205,-1637]$ |
$[-3200000/1637,-1200000/1637,-33600/1637]$ |
$y^2 + y = x^5 - x^4 + x^3 - x^2$ |
| 1643.a.1643.1 |
1643.a |
\( 31 \cdot 53 \) |
\( - 31 \cdot 53 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011228\) |
\(21.316178\) |
\(0.239346\) |
$[40,-1088,-3752,6572]$ |
$[20,198,-572,-12661,1643]$ |
$[3200000/1643,1584000/1643,-228800/1643]$ |
$y^2 + y = x^5 + x^4 - 5x^3 + 5x^2 - 2x$ |
| 1647.a.1647.1 |
1647.a |
\( 3^{3} \cdot 61 \) |
\( 3^{3} \cdot 61 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.016225\) |
\(17.240672\) |
\(0.279723\) |
$[36,-639,16641,210816]$ |
$[9,30,-296,-891,1647]$ |
$[2187/61,810/61,-888/61]$ |
$y^2 + (x^3 + x + 1)y = x^5$ |
| 1701.a.1701.1 |
1701.a |
\( 3^{5} \cdot 7 \) |
\( 3^{5} \cdot 7 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.723792\) |
\(0.723792\) |
$[84128,228576,6363290016,28]$ |
$[126192,663174672,4644628928416,36578592038091072,1701]$ |
$[131690013992224449101824/7,16452745612696372576256/21,8218113979245079207936/189]$ |
$y^2 + y = x^5 + 19x^4 + 86x^3 - 60x^2 + 12x - 1$ |
| 1706.a.3412.1 |
1706.a |
\( 2 \cdot 853 \) |
\( 2^{2} \cdot 853 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005601\) |
\(25.509541\) |
\(0.285782\) |
$[304,1816,196969,-13648]$ |
$[152,660,-977,-146026,-3412]$ |
$[-20284203008/853,-579448320/853,5643152/853]$ |
$y^2 + (x + 1)y = x^6 - x^5 - x^4$ |
| 1717.b.1717.1 |
1717.b |
\( 17 \cdot 101 \) |
\( 17 \cdot 101 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017533\) |
\(16.401039\) |
\(0.287561\) |
$[40,844,12015,6868]$ |
$[20,-124,-535,-6519,1717]$ |
$[3200000/1717,-992000/1717,-214000/1717]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^3 - 2x^2 - x$ |
| 1721.a.1721.1 |
1721.a |
\( 1721 \) |
\( -1721 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009817\) |
\(25.739030\) |
\(0.252677\) |
$[108,2937,92403,220288]$ |
$[27,-92,-320,-4276,1721]$ |
$[14348907/1721,-1810836/1721,-233280/1721]$ |
$y^2 + (x^3 + 1)y = x^2 - x$ |
| 1753.a.1753.1 |
1753.a |
\( 1753 \) |
\( -1753 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011436\) |
\(22.364636\) |
\(0.255772\) |
$[108,1497,18531,224384]$ |
$[27,-32,256,1472,1753]$ |
$[14348907/1753,-629856/1753,186624/1753]$ |
$y^2 + (x^3 + 1)y = x^2$ |
| 1757.a.1757.1 |
1757.a |
\( 7 \cdot 251 \) |
\( 7 \cdot 251 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010713\) |
\(24.064792\) |
\(0.257806\) |
$[8,592,2392,-7028]$ |
$[4,-98,-156,-2557,-1757]$ |
$[-1024/1757,896/251,2496/1757]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^3 + x^2$ |
| 1777.a.1777.1 |
1777.a |
\( 1777 \) |
\( 1777 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039015\) |
\(7.694781\) |
\(0.300215\) |
$[6052,-1391,-2704039,227456]$ |
$[1513,95440,8030588,760371511,1777]$ |
$[7928565897078793/1777,330557651801680/1777,18383373101372/1777]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + 7x^2 - x - 8$ |
| 1797.a.5391.1 |
1797.a |
\( 3 \cdot 599 \) |
\( 3^{2} \cdot 599 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006312\) |
\(20.515245\) |
\(0.258986\) |
$[1300,-8375,-4993627,690048]$ |
$[325,4750,117316,3891300,5391]$ |
$[3625908203125/5391,163058593750/5391,12391502500/5391]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 4x^4 + 2x^3 + x^2$ |
