| 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 |
| 72448.a.72448.1 |
72448.a |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.518325\) |
\(16.750347\) |
\(2.170533\) |
$[34,-116,1826,283]$ |
$[68,502,-18100,-370701,72448]$ |
$[\frac{5679428}{283},\frac{1233163}{566},-\frac{1307725}{1132}]$ |
$y^2 = x^5 - x^3 - x + 1$ |
| 72448.b.72448.1 |
72448.b |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.108651\) |
\(2.777163\) |
$[232,640,62588,-283]$ |
$[464,7264,6144,-12478720,-72448]$ |
$[-\frac{84013666304}{283},-\frac{2834587136}{283},-\frac{5167104}{283}]$ |
$y^2 = x^5 + 3x^4 - 4x^2 + x + 2$ |
| 72448.c.72448.1 |
72448.c |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.716985\) |
\(2.179246\) |
$[16,-344,160,283]$ |
$[32,960,-9216,-304128,72448]$ |
$[\frac{131072}{283},\frac{122880}{283},-\frac{36864}{283}]$ |
$y^2 = x^5 + x^4 + x^2 - 1$ |
| 72448.d.72448.1 |
72448.d |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.605097\) |
\(1.901274\) |
$[34,-116,1826,283]$ |
$[68,502,-18100,-370701,72448]$ |
$[\frac{5679428}{283},\frac{1233163}{566},-\frac{1307725}{1132}]$ |
$y^2 = x^5 - x^3 - x - 1$ |
| 72448.e.72448.1 |
72448.e |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.391342\) |
\(15.037637\) |
\(1.471215\) |
$[1792,88,21656,-283]$ |
$[3584,534976,106646016,24005000192,-72448]$ |
$[-\frac{2309936491003904}{283},-\frac{96205153501184}{283},-\frac{5351070498816}{283}]$ |
$y^2 = x^5 - 3x^4 + 19x^2 + 22x + 7$ |
| 72448.f.72448.1 |
72448.f |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.359975\) |
\(2.089994\) |
$[64,88,1640,-283]$ |
$[128,448,1536,-1024,-72448]$ |
$[-\frac{134217728}{283},-\frac{3670016}{283},-\frac{98304}{283}]$ |
$y^2 = x^5 - 2x^3 - x^2 + x$ |
| 72448.g.72448.1 |
72448.g |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.460536\) |
\(4.232408\) |
\(2.603498\) |
$[1536,2280,1152096,-283]$ |
$[3072,387136,64104448,11763645440,-72448]$ |
$[-\frac{1068725302198272}{283},-\frac{43841683980288}{283},-\frac{2363146371072}{283}]$ |
$y^2 = x^5 + 7x^4 + 10x^3 - 8x^2 + x$ |
| 72448.h.72448.1 |
72448.h |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.463813\) |
\(2.615953\) |
$[94,-212,-7090,-283]$ |
$[188,2038,36276,666611,-72448]$ |
$[-\frac{917380028}{283},-\frac{105795637}{566},-\frac{20033421}{1132}]$ |
$y^2 = x^5 - 3x^3 + 2x^2 + x - 1$ |
| 72448.i.72448.1 |
72448.i |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.462799\) |
\(20.147994\) |
\(2.331120\) |
$[560,6904,1083520,-283]$ |
$[1120,33856,1274880,70409216,-72448]$ |
$[-\frac{6884147200000}{283},-\frac{185801728000}{283},-\frac{6246912000}{283}]$ |
$y^2 = x^5 + 4x^4 - 10x^2 - 2x + 7$ |
| 72448.j.72448.1 |
72448.j |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.882709\) |
\(11.503241\) |
\(2.538503\) |
$[72,-240,-6012,-283]$ |
$[144,1504,24064,300800,-72448]$ |
$[-\frac{241864704}{283},-\frac{17542656}{283},-\frac{1949184}{283}]$ |
$y^2 = x^5 - x^4 - 2x^3 + 3x^2 - 1$ |
| 72448.k.72448.1 |
72448.k |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.894065\) |
\(11.354683\) |
\(2.537957\) |
$[40,-80,-284,283]$ |
$[80,480,-1536,-88320,72448]$ |
$[\frac{12800000}{283},\frac{960000}{283},-\frac{38400}{283}]$ |
$y^2 = x^5 - x^2 - x$ |
| 72448.l.72448.1 |
72448.l |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.90.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.220933\) |
\(2.305233\) |
$[34,-92,178,283]$ |
$[68,438,-5172,-135885,72448]$ |
$[\frac{5679428}{283},\frac{1075947}{566},-\frac{373677}{1132}]$ |
$y^2 = x^5 + 2x^4 + x^3 - x - 1$ |
| 72448.m.72448.1 |
72448.m |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.177545\) |
\(6.987157\) |
\(2.056923\) |
$[110,244,7750,-283]$ |
$[220,1366,9300,45011,-72448]$ |
$[-\frac{2013137500}{283},-\frac{113634125}{566},-\frac{7033125}{1132}]$ |
$y^2 = x^5 - 3x^4 - x^3 + 3x^2 - x$ |
| 72448.n.72448.1 |
72448.n |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.111241\) |
\(2.027810\) |
$[120,144,5940,-283]$ |
$[240,2016,15360,-94464,-72448]$ |
$[-\frac{3110400000}{283},-\frac{108864000}{283},-\frac{3456000}{283}]$ |
$y^2 = x^5 - x^4 - 4x^3 + 4x^2 - x$ |
| 72448.o.72448.1 |
72448.o |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.220676\) |
\(3.877753\) |
\(2.152808\) |
$[240,2664,165960,-283]$ |
$[480,2496,23040,1207296,-72448]$ |
$[-\frac{99532800000}{283},-\frac{1078272000}{283},-\frac{20736000}{283}]$ |
$y^2 = x^5 - 7x^4 + 14x^3 - 8x^2 - x$ |
| 72448.p.72448.1 |
72448.p |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.029659\) |
\(8.692327\) |
\(2.237534\) |
$[64,-56,296,283]$ |
$[128,832,-2560,-254976,72448]$ |
$[\frac{134217728}{283},\frac{6815744}{283},-\frac{163840}{283}]$ |
$y^2 = x^5 + x^4 - x^2 - 2x - 1$ |
| 72448.q.72448.1 |
72448.q |
\( 2^{8} \cdot 283 \) |
\( - 2^{8} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.546294\) |
\(13.001393\) |
\(1.775646\) |
$[94,-212,-7090,-283]$ |
$[188,2038,36276,666611,-72448]$ |
$[-\frac{917380028}{283},-\frac{105795637}{566},-\frac{20033421}{1132}]$ |
$y^2 = x^5 - 3x^3 - 2x^2 + x + 1$ |
| 72448.r.289792.1 |
72448.r |
\( 2^{8} \cdot 283 \) |
\( - 2^{10} \cdot 283 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.097829\) |
\(16.948027\) |
\(1.658008\) |
$[250,880,88864,1132]$ |
$[500,8070,-16644,-18361725,289792]$ |
$[\frac{30517578125}{283},\frac{7880859375}{2264},-\frac{65015625}{4528}]$ |
$y^2 = x^6 - x^4 - x^3 - x^2 + x + 1$ |
| 72448.s.289792.1 |
72448.s |
\( 2^{8} \cdot 283 \) |
\( - 2^{10} \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.198311\) |
\(10.604191\) |
\(2.102933\) |
$[390,-576,-76320,-1132]$ |
$[780,26886,1308420,74427651,-289792]$ |
$[-\frac{281950621875}{283},-\frac{99678164625}{2264},-\frac{12438167625}{4528}]$ |
$y^2 = x^6 - 3x^4 - x^3 + 3x^2 + x - 1$ |
