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 |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[136,280,15060,1856]$ |
$[68,146,-64,-6417,464]$ |
$[90870848/29,2869192/29,-18496/29]$ |
$y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$ |
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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.278318\) |
\(0.227447\) |
$[152,17065,1592025,7552]$ |
$[152,-10414,-926656,-62325777,60416]$ |
$[79235168/59,-35714813/59,-20907676/59]$ |
$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.812569\) |
\(0.293946\) |
$[104,-824,-20333,-2764]$ |
$[52,250,601,-7812,-691]$ |
$[-380204032/691,-35152000/691,-1625104/691]$ |
$y^2 + (x + 1)y = x^5 - x^3 - x^2$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.361162\) |
\(0.286893\) |
$[160,-1280,-42089,2836]$ |
$[80,480,1121,-35180,709]$ |
$[3276800000/709,245760000/709,7174400/709]$ |
$y^2 + xy = x^5 - 2x^2 + x$ |
720.a.6480.1 |
720.a |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.444268\) |
\(0.295133\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$ |
807.a.2421.1 |
807.a |
\( 3 \cdot 269 \) |
\( 3^{2} \cdot 269 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.761140\) |
\(0.305036\) |
$[680,640,153059,9684]$ |
$[340,4710,84049,1598140,2421]$ |
$[4543542400000/2421,61707280000/807,9716064400/2421]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$ |
832.a.832.1 |
832.a |
\( 2^{6} \cdot 13 \) |
\( - 2^{6} \cdot 13 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.148215\) |
\(0.330441\) |
$[272,-131,-12402,-104]$ |
$[272,3170,51008,956319,-832]$ |
$[-23262937088/13,-996749440/13,-58965248/13]$ |
$y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$ |
834.a.1668.1 |
834.a |
\( 2 \cdot 3 \cdot 139 \) |
\( 2^{2} \cdot 3 \cdot 139 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.763516\) |
\(0.367610\) |
$[372,3345,401289,213504]$ |
$[93,221,-111,-14791,1668]$ |
$[2318961231/556,59254299/556,-320013/556]$ |
$y^2 + (x^3 + 1)y = -x^2 + x - 1$ |
847.c.9317.1 |
847.c |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.983400\) |
\(0.311981\) |
$[424,3520,581427,37268]$ |
$[212,1286,-7999,-837396,9317]$ |
$[428232184832/9317,12253172608/9317,-359507056/9317]$ |
$y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$ |
862.a.862.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2 \cdot 431 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[1940,2609665,270472593,-110336]$ |
$[485,-98935,11156681,-1094285985,-862]$ |
$[-26835438303125/862,11286912906875/862,-2624330288225/862]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$ |
882.a.302526.1 |
882.a |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( - 2 \cdot 3^{2} \cdot 7^{5} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.542623\) |
\(0.391957\) |
$[2572,-283391,165464399,38723328]$ |
$[643,29035,-3791761,-820283387,302526]$ |
$[109914468611443/302526,7718888172745/302526,-1567699793689/302526]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$ |
909.a.909.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{2} \cdot 101 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[40,-200,-5469,3636]$ |
$[20,50,441,1580,909]$ |
$[3200000/909,400000/909,19600/101]$ |
$y^2 + (x^3 + x)y = -x^4 + x^2 - x$ |
925.a.925.1 |
925.a |
\( 5^{2} \cdot 37 \) |
\( 5^{2} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[40,-944,-14117,3700]$ |
$[20,174,713,-4004,925]$ |
$[128000/37,55680/37,11408/37]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$ |
930.a.930.1 |
930.a |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.846489\) |
\(0.388226\) |
$[46596,239073,3674852529,119040]$ |
$[11649,5644172,3640360380,2637470125259,930]$ |
$[71502622649365111083/310,1487013548016809538/155,531176338621566]$ |
$y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$ |
936.a.1872.1 |
936.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(7.131061\) |
\(0.445691\) |
$[45352,11224,169415364,7488]$ |
$[22676,21423170,26983749312,38232821637503,1872]$ |
$[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ |
$y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$ |
960.a.245760.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[120,213,10095,30]$ |
$[480,7328,-15360,-15268096,245760]$ |
$[103680000,3297600,-14400]$ |
$y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$ |
960.a.368640.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[24952719973569408/5,1038436236963696/5,11510985848256]$ |
$y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$ |
960.a.983040.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[9,33,666,120]$ |
$[36,-298,-34260,-330541,983040]$ |
$[19683/320,-36207/2560,-46251/1024]$ |
$y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$ |
990.a.8910.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{4} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.174937\) |
\(0.385934\) |
$[3268,252577,318023313,1140480]$ |
$[817,17288,-766260,-231227341,8910]$ |
$[364007458703857/8910,4713906106372/4455,-57404054]$ |
$y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$ |
997.a.997.1 |
997.a |
\( 997 \) |
\( 997 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[6112,48064,98113399,3988]$ |
$[3056,381120,61964417,11027700988,997]$ |
$[266542673508171776/997,10877317101649920/997,578694117523712/997]$ |
$y^2 + xy = x^5 - 8x^4 + 16x^3 - x$ |
997.a.997.2 |
997.a |
\( 997 \) |
\( 997 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[64,184,391,3988]$ |
$[32,12,305,2404,997]$ |
$[33554432/997,393216/997,312320/997]$ |
$y^2 + (x + 1)y = x^5 + x^4$ |
1050.a.131250.1 |
1050.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.612551\) |
\(0.413284\) |
$[11868,198609,759217863,16800000]$ |
$[2967,358520,56735700,9949557875,131250]$ |
$[76641937806559869/43750,312136655012892/4375,475666111026/125]$ |
$y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$ |
1051.b.1051.1 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.331720\) |
\(0.364558\) |
$[64,-200,185,4204]$ |
$[32,76,-241,-3372,1051]$ |
$[33554432/1051,2490368/1051,-246784/1051]$ |
$y^2 + (x + 1)y = -x^5 - x^4$ |
1123.a.1123.1 |
1123.a |
\( 1123 \) |
\( -1123 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.491845\) |
\(0.335810\) |
$[24,-672,-75,4492]$ |
$[12,118,-361,-4564,1123]$ |
$[248832/1123,203904/1123,-51984/1123]$ |
$y^2 + (x^3 + x)y = -x^4 - x^2 - x$ |
1147.a.35557.1 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.458568\) |
\(0.358080\) |
$[3712,11944,14677639,142228]$ |
$[1856,141540,14195057,1578113548,35557]$ |
$[22023678539595776/35557,904926084464640/35557,48898223869952/35557]$ |
$y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$ |
1152.a.147456.1 |
1152.a |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.270694\) |
\(0.454418\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 - 2x^4 + 2x^2 - 1$ |
1176.a.2352.1 |
1176.a |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.624711\) |
\(0.394522\) |
$[1032,984,324564,9408]$ |
$[516,10930,305472,9539663,2352]$ |
$[762091768512/49,31284414360/49,1694453184/49]$ |
$y^2 + (x^3 + x)y = x^4 + 3x^2 + 3$ |
1184.a.2368.1 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( 2^{6} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.232044\) |
\(0.444751\) |
$[128,16,1208,296]$ |
$[128,672,4160,20224,2368]$ |
$[536870912/37,22020096/37,1064960/37]$ |
$y^2 + y = 2x^5 + x^4 + x^2 + x$ |
1184.a.606208.2 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( - 2^{14} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.116022\) |
\(0.444751\) |
$[352,316,34242,74]$ |
$[1408,79232,5831680,483323904,606208]$ |
$[337748426752/37,13498597376/37,705633280/37]$ |
$y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$ |
1225.a.6125.1 |
1225.a |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{3} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.72.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.927897\) |
\(0.372747\) |
$[320,14344,962481,-24500]$ |
$[160,-1324,8791,-86604,-6125]$ |
$[-838860800/49,43384832/49,-9001984/245]$ |
$y^2 + (x^3 + x^2)y = 2x^3 + x^2 + x + 2$ |
1309.a.9163.1 |
1309.a |
\( 7 \cdot 11 \cdot 17 \) |
\( - 7^{2} \cdot 11 \cdot 17 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.545616\) |
\(0.423301\) |
$[1696,-7904,-4279929,-36652]$ |
$[848,31280,1576817,89675604,-9163]$ |
$[-438509757267968/9163,-1122032353280/539,-103081401088/833]$ |
$y^2 + (x^2 + 1)y = 7x^5 - x^4 - 5x^3 - x^2 + x$ |
1320.a.2640.1 |
1320.a |
\( 2^{3} \cdot 3 \cdot 5 \cdot 11 \) |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.746741\) |
\(0.554586\) |
$[63768,10392,220729308,10560]$ |
$[31884,42356162,75020763840,149479393726079,2640]$ |
$[686471900571962215488/55,28601826290311163976/55,28888377841215936]$ |
$y^2 + (x^3 + x)y = -x^6 + 9x^4 - 40x^2 + 55$ |
1344.a.4032.1 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( - 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.691213\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$ |
1344.a.4032.2 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.382426\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 + 12x^4 - 48x^2 + 63$ |
1344.b.172032.1 |
1344.b |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.087817\) |
\(0.471494\) |
$[4248,2904,4071996,672]$ |
$[8496,2999840,1408899072,742741622528,172032]$ |
$[1801197437083776/7,74856652932240/7,591152665536]$ |
$y^2 = x^5 - 11x^4 + 32x^3 - 11x^2 + x$ |
1376.a.2752.1 |
1376.a |
\( 2^{5} \cdot 43 \) |
\( - 2^{6} \cdot 43 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.493471\) |
\(0.452921\) |
$[192,-528,-2760,-344]$ |
$[192,1888,64,-888064,-2752]$ |
$[-4076863488/43,-208797696/43,-36864/43]$ |
$y^2 + y = 2x^5 + 3x^4 - 2x^2$ |
1408.b.180224.1 |
1408.b |
\( 2^{7} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.656364\) |
\(0.478523\) |
$[80,280,8718,22]$ |
$[320,1280,-154624,-12779520,180224]$ |
$[204800000/11,2560000/11,-966400/11]$ |
$y^2 = 2x^5 + 2x^4 + 4x^3 + 3x^2 + 2x + 1$ |
1408.b.720896.1 |
1408.b |
\( 2^{7} \cdot 11 \) |
\( - 2^{16} \cdot 11 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.312728\) |
\(0.478523\) |
$[680,32140,5350958,-88]$ |
$[2720,-34560,1197056,515399680,-720896]$ |
$[-2271771200000/11,10612080000/11,-135136400/11]$ |
$y^2 + y = 4x^5 + 17x^4 - 8x^3 - 3x^2 + x$ |
1408.b.720896.2 |
1408.b |
\( 2^{7} \cdot 11 \) |
\( - 2^{16} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.656364\) |
\(0.478523\) |
$[32,-80,-1240,-88]$ |
$[128,1536,45056,851968,-720896]$ |
$[-524288/11,-49152/11,-1024]$ |
$y^2 = x^5 + 2x^3 - 4x^2 + x$ |
1470.a.2940.1 |
1470.a |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
\( - 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(8.519256\) |
\(0.532453\) |
$[2556,6897,5825079,376320]$ |
$[639,16726,574080,21769511,2940]$ |
$[35512646315733/980,727349955399/490,3906815328/49]$ |
$y^2 + (x^2 + x)y = -x^6 + 2x^5 - 5x^4 + 4x^3 - 5x^2 + 2x - 1$ |
1472.a.5888.1 |
1472.a |
\( 2^{6} \cdot 23 \) |
\( - 2^{8} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.717638\) |
\(0.491176\) |
$[2,-56,74,23]$ |
$[4,150,-692,-6317,5888]$ |
$[4/23,75/46,-173/92]$ |
$y^2 = x^5 + x^4 - x^3 - 2x^2 - x$ |
1472.a.94208.2 |
1472.a |
\( 2^{6} \cdot 23 \) |
\( - 2^{12} \cdot 23 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.717638\) |
\(0.491176\) |
$[256,-116,-128996,-368]$ |
$[512,11232,1184000,120012544,-94208]$ |
$[-8589934592/23,-368050176/23,-75776000/23]$ |
$y^2 + y = 4x^5 + x^4 + 4x^2 + 2x$ |
1534.a.3068.1 |
1534.a |
\( 2 \cdot 13 \cdot 59 \) |
\( - 2^{2} \cdot 13 \cdot 59 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.954974\) |
\(0.498593\) |
$[2228,-11087,-8234503,-392704]$ |
$[557,13389,442913,16859305,-3068]$ |
$[-53613724194557/3068,-2313735590577/3068,-2329039243/52]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^3 - x^2 + 4x - 1$ |
1536.b.49152.2 |
1536.b |
\( 2^{9} \cdot 3 \) |
\( - 2^{14} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.996682\) |
\(0.499793\) |
$[624,141,29202,6]$ |
$[2496,258080,35377152,5424021248,49152]$ |
$[1970977701888,81648253440,4484054016]$ |
$y^2 + x^3y = 3x^4 + 11x^2 + 12$ |
1536.c.98304.1 |
1536.c |
\( 2^{9} \cdot 3 \) |
\( 2^{15} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.680538\) |
\(0.552517\) |
$[1068,38019,11064156,12]$ |
$[4272,354880,32280576,2990701568,98304]$ |
$[14473882091808,281451823560,5992838496]$ |
$y^2 + y = 4x^6 - 12x^5 + 3x^4 + 14x^3 - 5x^2 - 4x + 1$ |
1573.b.224939.1 |
1573.b |
\( 11^{2} \cdot 13 \) |
\( - 11^{3} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.742030\) |
\(0.608877\) |
$[472,-4796,-683705,-899756]$ |
$[236,3120,53993,751987,-224939]$ |
$[-732082482176/224939,-3154621440/17303,-3007194128/224939]$ |
$y^2 + (x + 1)y = x^5 + x^4 - 5x^3 + 3x^2 - 1$ |
1584.a.684288.1 |
1584.a |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{5} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(4.753791\) |
\(0.594224\) |
$[7444,76621,183223627,85536]$ |
$[7444,2257800,897608448,396034111728,684288]$ |
$[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ |
$y^2 + (x^3 + x)y = -x^6 + 6x^4 - 17x^2 + 11$ |
1656.a.804816.1 |
1656.a |
\( 2^{3} \cdot 3^{2} \cdot 23 \) |
\( 2^{4} \cdot 3^{7} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(5.200244\) |
\(0.650030\) |
$[680,19992,5459780,13248]$ |
$[1020,13362,-5426240,-1428326961,804816]$ |
$[283971400000/207,10941251000/621,-39204584000/5589]$ |
$y^2 + xy = 2x^5 - 6x^4 + 13x^3 - 13x^2 + 9x$ |
1680.a.16800.1 |
1680.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.090690\) |
\(0.636336\) |
$[404040,44088,5935895700,67200]$ |
$[202020,1700496002,19085068732800,240969733145567999,16800]$ |
$[20029151526577171524000,834544374130868293620,46363176164438078400]$ |
$y^2 + (x^3 + x)y = -x^6 - 18x^4 - 136x^2 - 350$ |
1800.a.3600.1 |
1800.a |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.5, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.948999\) |
\(0.435906\) |
$[280,856,70812,14400]$ |
$[140,674,4032,27551,3600]$ |
$[134456000/9,4623640/9,21952]$ |
$y^2 + (x^3 + x)y = -x^4 + x^2 - 1$ |