| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.970596\) |
\(0.189706\) |
$[344,-3068,-526433,-47916]$ |
$[172,1744,45841,1210779,-11979]$ |
$[-150536645632/11979,-8874253312/11979,-1356160144/11979]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(29.113273\) |
\(0.227447\) |
$[280,760,60604,-3776]$ |
$[140,690,4544,40015,-944]$ |
$[-3361400000/59,-118335000/59,-5566400/59]$ |
$y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.692472\) |
\(0.256925\) |
$[1264,18124,6869487,33300]$ |
$[632,13622,351361,9125317,8325]$ |
$[100828984082432/8325,3438682756096/8325,140342016064/8325]$ |
$y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.976027\) |
\(0.332667\) |
$[134,-464,-15328,-176]$ |
$[268,4230,61444,-356477,-45056]$ |
$[-1350125107/44,-636113745/352,-68955529/704]$ |
$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.756843\) |
\(0.293076\) |
$[576,-840,740385,115596]$ |
$[288,3596,-38169,-5980972,28899]$ |
$[220150628352/3211,9544531968/3211,-351765504/3211]$ |
$y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$ |
| 762.a.82296.1 |
762.a |
\( 2 \cdot 3 \cdot 127 \) |
\( 2^{3} \cdot 3^{4} \cdot 127 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.733449\) |
\(0.348614\) |
$[12004,205249,810020577,10533888]$ |
$[3001,366698,58441312,10228738527,82296]$ |
$[243405270090015001/82296,4955375073324349/41148,65790314289164/10287]$ |
$y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x$ |
| 784.c.614656.1 |
784.c |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.5760.7 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 826.a.11564.1 |
826.a |
\( 2 \cdot 7 \cdot 59 \) |
\( - 2^{2} \cdot 7^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.174483\) |
\(0.365958\) |
$[92,-554591,-3126961,1480192]$ |
$[23,23130,-104176,-134348237,11564]$ |
$[6436343/11564,140711355/5782,-13777276/2891]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$ |
| 830.a.830000.1 |
830.a |
\( 2 \cdot 5 \cdot 83 \) |
\( - 2^{4} \cdot 5^{4} \cdot 83 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.868729\) |
\(0.366796\) |
$[15236,-229487,-1147645831,-106240000]$ |
$[3809,614082,133745600,33085071919,-830000]$ |
$[-801779343712318049/830000,-16967946642572289/415000,-4851113741084/2075]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x$ |
| 856.a.1712.1 |
856.a |
\( 2^{3} \cdot 107 \) |
\( - 2^{4} \cdot 107 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.653846\) |
\(0.314637\) |
$[32,-368,-11044,-6848]$ |
$[16,72,964,2560,-1712]$ |
$[-65536/107,-18432/107,-15424/107]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x$ |
| 862.a.6896.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2^{4} \cdot 431 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[932,12385,3688145,-882688]$ |
$[233,1746,11456,-94817,-6896]$ |
$[-686719856393/6896,-11042871201/3448,-38870924/431]$ |
$y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$ |
| 909.a.8181.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{4} \cdot 101 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[1384,44560,19431635,32724]$ |
$[692,12526,35569,-33071732,8181]$ |
$[158683025503232/8181,4150789321088/8181,17032713616/8181]$ |
$y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$ |
| 925.a.23125.1 |
925.a |
\( 5^{2} \cdot 37 \) |
\( 5^{4} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[3496,50536,55764955,92500]$ |
$[1748,118890,10257041,948618892,23125]$ |
$[16319511005139968/23125,126998797147776/4625,31340429803664/23125]$ |
$y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.589621\) |
\(0.337338\) |
$[6112,48064,98113399,3988]$ |
$[3056,381120,61964417,11027700988,997]$ |
$[266542673508171776/997,10877317101649920/997,578694117523712/997]$ |
$y^2 + xy = x^5 - 8x^4 + 16x^3 - x$ |
| 1051.b.1051.2 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.832930\) |
\(0.364558\) |
$[6176,-50240,-103225225,-4204]$ |
$[3088,405696,72449921,14784027908,-1051]$ |
$[-280793117300359168/1051,-11946277554880512/1051,-690863899476224/1051]$ |
$y^2 + xy = x^5 + 8x^4 + 16x^3 + x$ |
| 1125.a.151875.1 |
1125.a |
\( 3^{2} \cdot 5^{3} \) |
\( - 3^{5} \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(1.964402\) |
\(0.491100\) |
$[8600,612100,1556297975,-607500]$ |
$[4300,668400,132975225,31258726875,-151875]$ |
$[-2352135088000000/243,-28342655360000/81,-437104339600/27]$ |
$y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.458568\) |
\(0.358080\) |
$[3712,11944,14677639,142228]$ |
$[1856,141540,14195057,1578113548,35557]$ |
$[22023678539595776/35557,904926084464640/35557,48898223869952/35557]$ |
$y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$ |
| 1147.a.35557.2 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.864642\) |
\(0.358080\) |
$[12352,2309104,8338761079,142228]$ |
$[6176,1204440,279006977,68117844088,35557]$ |
$[8985379753611493376/35557,283731159059005440/35557,10642156427543552/35557]$ |
$y^2 + xy = x^5 + 6x^4 - 32x^2 + x$ |
| 1184.a.606208.1 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( 2^{14} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(14.232044\) |
\(0.444751\) |
$[176,496,29918,74]$ |
$[704,15360,140288,-34291712,606208]$ |
$[10554638336/37,327106560/37,4243712/37]$ |
$y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$ |
| 1272.a.122112.1 |
1272.a |
\( 2^{3} \cdot 3 \cdot 53 \) |
\( - 2^{8} \cdot 3^{2} \cdot 53 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.397916\) |
\(0.399942\) |
$[124,-5027,-35457,15264]$ |
$[124,3992,-79504,-6448640,122112]$ |
$[114516604/477,29731418/477,-4775209/477]$ |
$y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$ |
| 1296.a.20736.1 |
1296.a |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 1311.a.814131.1 |
1311.a |
\( 3 \cdot 19 \cdot 23 \) |
\( - 3^{4} \cdot 19 \cdot 23^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.753499\) |
\(0.429797\) |
$[600,2040,860349,3256524]$ |
$[300,3410,-4761,-3264100,814131]$ |
$[30000000000/10051,3410000000/30153,-10000/19]$ |
$y^2 + xy = x^5 + 5x^4 + 5x^3 + 4x^2 + x$ |
| 1338.b.72252.1 |
1338.b |
\( 2 \cdot 3 \cdot 223 \) |
\( 2^{2} \cdot 3^{4} \cdot 223 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.653207\) |
\(0.490367\) |
$[9956,4983313,12890442777,9248256]$ |
$[2489,50492,218356,-501488495,72252]$ |
$[95526635745351449/72252,194642319821287/18063,338185460269/18063]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 4x^3 - 12x^2 - 6x + 5$ |
| 1408.b.180224.2 |
1408.b |
\( 2^{7} \cdot 11 \) |
\( - 2^{14} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(15.312728\) |
\(0.478523\) |
$[128,-20,-2290,-22]$ |
$[512,11136,410624,21557248,-180224]$ |
$[-2147483648/11,-91226112/11,-6569984/11]$ |
$y^2 = 2x^5 - 4x^3 - x^2 + 2x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.656364\) |
\(0.478523\) |
$[32,-80,-1240,-88]$ |
$[128,1536,45056,851968,-720896]$ |
$[-524288/11,-49152/11,-1024]$ |
$y^2 = x^5 + 2x^3 - 4x^2 + x$ |
| 1416.a.8496.1 |
1416.a |
\( 2^{3} \cdot 3 \cdot 59 \) |
\( - 2^{4} \cdot 3^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.958620\) |
\(0.415517\) |
$[256,-2144,-178692,-33984]$ |
$[128,1040,12004,113728,-8496]$ |
$[-2147483648/531,-136314880/531,-12292096/531]$ |
$y^2 + (x^3 + x)y = x^5 - x^3 - 1$ |
| 1416.b.135936.1 |
1416.b |
\( 2^{3} \cdot 3 \cdot 59 \) |
\( - 2^{8} \cdot 3^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 7 \) |
\(1.000000\) |
\(15.707538\) |
\(0.560984\) |
$[192,-96,90660,543744]$ |
$[96,400,-8452,-242848,135936]$ |
$[3538944/59,153600/59,-33808/59]$ |
$y^2 + (x^3 + x)y = -2x^4 - x^3 + x + 1$ |
| 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.94208.1 |
1472.a |
\( 2^{6} \cdot 23 \) |
\( - 2^{12} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(3.929409\) |
\(0.491176\) |
$[1168,1204,381076,-368]$ |
$[2336,224160,28881152,4304666368,-94208]$ |
$[-16982602489856/23,-697616405760/23,-38476914752/23]$ |
$y^2 = 4x^5 - 3x^4 - 4x^3 - x^2 + 7x - 3$ |
| 1488.a.71424.1 |
1488.a |
\( 2^{4} \cdot 3 \cdot 31 \) |
\( - 2^{8} \cdot 3^{2} \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.909626\) |
\(0.496234\) |
$[34,-104,-438,279]$ |
$[68,470,-1396,-78957,71424]$ |
$[5679428/279,1154555/558,-100861/1116]$ |
$y^2 = x^5 - x^3 - x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.742030\) |
\(0.608877\) |
$[472,-4796,-683705,-899756]$ |
$[236,3120,53993,751987,-224939]$ |
$[-732082482176/224939,-3154621440/17303,-3007194128/224939]$ |
$y^2 + (x + 1)y = x^5 + x^4 - 5x^3 + 3x^2 - 1$ |
| 1717.a.1717.2 |
1717.a |
\( 17 \cdot 101 \) |
\( 17 \cdot 101 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.212340\) |
\(0.638271\) |
$[4624,118708,196323055,6868]$ |
$[2312,202938,19499969,975024121,1717]$ |
$[3885887537053696/101,147529185211392/101,60707071808]$ |
$y^2 + xy = x^5 + 9x^4 + 24x^3 + 16x^2 + x$ |
| 1740.a.104400.1 |
1740.a |
\( 2^{2} \cdot 3 \cdot 5 \cdot 29 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.116047\) |
\(0.568450\) |
$[28100,7231657,99549877317,-13363200]$ |
$[7025,1754957,7872289,-756142810406,-104400]$ |
$[-684371056797265625/4176,-24336911168273125/4176,-15540095293225/4176]$ |
$y^2 + (x^2 + x)y = 2x^5 - 14x^3 - 5x^2 + 30x$ |
| 1770.a.26550.1 |
1770.a |
\( 2 \cdot 3 \cdot 5 \cdot 59 \) |
\( - 2 \cdot 3^{2} \cdot 5^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.809597\) |
\(0.522489\) |
$[8740,87985,236184393,-3398400]$ |
$[2185,195260,23092156,3082473315,-26550]$ |
$[-1992127808244625/1062,-40737803081950/531,-2204942969582/531]$ |
$y^2 + (x^2 + x)y = 3x^5 - 7x^3 + 7x + 3$ |
| 1832.a.3664.1 |
1832.a |
\( 2^{3} \cdot 229 \) |
\( 2^{4} \cdot 229 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.951866\) |
\(0.654746\) |
$[1048,8344,3077980,14656]$ |
$[524,10050,193472,94207,3664]$ |
$[2469087337664/229,90373258200/229,3320172992/229]$ |
$y^2 + xy = 2x^5 + 4x^4 - x^3 - 3x^2 + x$ |
| 1832.b.14656.1 |
1832.b |
\( 2^{3} \cdot 229 \) |
\( 2^{6} \cdot 229 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(21.492106\) |
\(0.671628\) |
$[544,4240,755740,58624]$ |
$[272,2376,16004,-323072,14656]$ |
$[23262937088/229,747090432/229,18500624/229]$ |
$y^2 + (x + 1)y = 2x^5 - 4x^3 - 2x^2$ |
| 1888.a.241664.1 |
1888.a |
\( 2^{5} \cdot 59 \) |
\( - 2^{12} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.762943\) |
\(0.610184\) |
$[32,-224,-796,944]$ |
$[64,768,-4352,-217088,241664]$ |
$[262144/59,49152/59,-4352/59]$ |
$y^2 = x^5 - x^4 - 2x^3 - x^2 - x$ |
| 1896.a.728064.1 |
1896.a |
\( 2^{3} \cdot 3 \cdot 79 \) |
\( 2^{10} \cdot 3^{2} \cdot 79 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 5 \) |
\(1.000000\) |
\(12.994338\) |
\(0.649717\) |
$[2020,7285,4913237,91008]$ |
$[2020,165160,17437456,1986458880,728064]$ |
$[32844064065625/711,2658820518125/1422,277936701025/2844]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 11x - 3$ |
| 1922.a.3844.1 |
1922.a |
\( 2 \cdot 31^{2} \) |
\( 2^{2} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(19.526754\) |
\(0.610211\) |
$[1220,20305,8995673,492032]$ |
$[305,3030,12416,-1348505,3844]$ |
$[2639363440625/3844,42984526875/1922,288749600/961]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 - 3x^3 - 2x^2 + 2x$ |
| 1944.a.34992.1 |
1944.a |
\( 2^{3} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{7} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.1920.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.436286\) |
\(0.476512\) |
$[224,-432,-16812,-576]$ |
$[336,5352,77764,-628800,-34992]$ |
$[-1101463552/9,-156649472/27,-60966976/243]$ |
$y^2 + xy = 2x^5 + 2x^4 - 3x^2 + x$ |
| 1947.a.578259.1 |
1947.a |
\( 3 \cdot 11 \cdot 59 \) |
\( - 3^{4} \cdot 11^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(2.369892\) |
\(0.592473\) |
$[2084,92089,-1192689283,-74017152]$ |
$[521,7473,17447797,2258614127,-578259]$ |
$[-38387392786601/578259,-352279115651/192753,-4736047465477/578259]$ |
$y^2 + (x^2 + x)y = x^5 + 2x^4 + x^3 - 16x^2 - 8x - 1$ |
| 2121.a.400869.1 |
2121.a |
\( 3 \cdot 7 \cdot 101 \) |
\( 3^{4} \cdot 7^{2} \cdot 101 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(16.927242\) |
\(0.528976\) |
$[1440,59280,25449111,1603476]$ |
$[720,11720,12321,-32121820,400869]$ |
$[2388787200000/4949,54005760000/4949,78854400/4949]$ |
$y^2 + xy = x^5 - 2x^4 - 4x^3 + 8x^2 - 1$ |
| 2123.a.409739.1 |
2123.a |
\( 11 \cdot 193 \) |
\( - 11 \cdot 193^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.583418\) |
\(0.697927\) |
$[304,8836,508207,-1638956]$ |
$[152,-510,13841,460933,-409739]$ |
$[-81136812032/409739,1791022080/409739,-319782464/409739]$ |
$y^2 + xy = x^5 - 5x^4 + 4x^3 - x$ |
| 2154.a.465264.1 |
2154.a |
\( 2 \cdot 3 \cdot 359 \) |
\( 2^{4} \cdot 3^{4} \cdot 359 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(10.287792\) |
\(0.642987\) |
$[9252,1337505,4613040945,59553792]$ |
$[2313,167186,380736,-6767629057,465264]$ |
$[817321917038553/5744,12770614373841/2872,1571702004/359]$ |
$y^2 + (x^2 + x)y = x^5 - 9x^3 - x^2 + 18x - 1$ |
| 2208.b.847872.1 |
2208.b |
\( 2^{5} \cdot 3 \cdot 23 \) |
\( - 2^{12} \cdot 3^{2} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(7.533472\) |
\(0.627789\) |
$[598,-5348,-286836,-3312]$ |
$[1196,73862,1261924,-986583485,-847872]$ |
$[-103903004413/36,-42921688303/288,-1226274647/576]$ |
$y^2 = 3x^5 - 4x^4 - 3x^3 + x^2 + 4x$ |
| 2272.a.36352.1 |
2272.a |
\( 2^{5} \cdot 71 \) |
\( 2^{9} \cdot 71 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(4.113550\) |
\(0.514194\) |
$[53576,333841,6003461273,4544]$ |
$[53576,119376930,353957026832,1178187563331583,36352]$ |
$[862147292483354448448/71,35855955716164159890/71,1984363130952884386/71]$ |
$y^2 + xy = 4x^5 + 31x^4 + 56x^3 - 16x^2 + x$ |
| 2288.a.805376.1 |
2288.a |
\( 2^{4} \cdot 11 \cdot 13 \) |
\( - 2^{9} \cdot 11^{2} \cdot 13 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(11.899789\) |
\(0.743737\) |
$[172,-4595,-143915,100672]$ |
$[172,4296,-6656,-4900112,805376]$ |
$[294016886/1573,42695259/1573,-29584/121]$ |
$y^2 + (x + 1)y = -4x^5 - x^4 - x^3 - x^2$ |
| 2534.a.17738.1 |
2534.a |
\( 2 \cdot 7 \cdot 181 \) |
\( - 2 \cdot 7^{2} \cdot 181 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.444781\) |
\(0.680598\) |
$[10148,-44783,-164789095,-2270464]$ |
$[2537,270048,38772524,6359992771,-17738]$ |
$[-105099908058856457/17738,-2204816098290672/8869,-2546472158422/181]$ |
$y^2 + (x^2 + x)y = x^5 + 6x^4 + 18x^3 + 8x^2 + x$ |
