| 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 |
| 62208.a.124416.1 |
62208.a |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{9} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.320.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(2.171851\) |
\(11.642472\) |
\(2.107143\) |
$[128,-1827,-133803,-2]$ |
$[768,68424,17384512,2167365360,-124416]$ |
$[-2147483648,-\frac{747372544}{3},-\frac{2225217536}{27}]$ |
$y^2 + x^3y = x^5 - x^4 - 2x^3 + 10x^2 - 4x - 6$ |
| 62208.b.124416.1 |
62208.b |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{9} \cdot 3^{5} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1, 3.320.6 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(11.642472\) |
\(1.455309\) |
$[128,-1827,-133803,-2]$ |
$[768,68424,17384512,2167365360,-124416]$ |
$[-2147483648,-\frac{747372544}{3},-\frac{2225217536}{27}]$ |
$y^2 + y = 2x^6 - 4x^5 - 2x^4 + 2x^3 + 5x^2 + x - 1$ |
| 62208.c.124416.1 |
62208.c |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{9} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.811391\) |
\(2.787361\) |
\(1.696230\) |
$[4032,8757,11342799,-486]$ |
$[8064,2686152,1185506368,586127696112,-124416]$ |
$[-274079378571264,-11321550471168,-\frac{1858873985024}{3}]$ |
$y^2 + x^3y = x^5 - 3x^4 - 10x^3 + 14x^2 + 24x - 30$ |
| 62208.d.186624.1 |
62208.d |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.839821\) |
\(1.604978\) |
$[42,48,606,3]$ |
$[252,1494,1332,-474093,186624]$ |
$[5445468,\frac{256221}{2},\frac{1813}{4}]$ |
$y^2 = x^5 + x^4 - 3x^3 - 2x^2 + x$ |
| 62208.e.186624.1 |
62208.e |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.792979\) |
\(1.974122\) |
$[462,2304,361170,729]$ |
$[924,29430,834772,-23698893,186624]$ |
$[\frac{10827136628}{3},\frac{248810485}{2},\frac{1237340797}{324}]$ |
$y^2 = x^5 - 6x^4 + 9x^3 + x^2 - 3x$ |
| 62208.f.186624.1 |
62208.f |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.082548\) |
\(1.135319\) |
$[462,2304,361170,729]$ |
$[924,29430,834772,-23698893,186624]$ |
$[\frac{10827136628}{3},\frac{248810485}{2},\frac{1237340797}{324}]$ |
$y^2 = x^5 + 6x^4 + 9x^3 - x^2 - 3x$ |
| 62208.g.186624.1 |
62208.g |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.636780\) |
\(2.204598\) |
$[42,48,606,3]$ |
$[252,1494,1332,-474093,186624]$ |
$[5445468,\frac{256221}{2},\frac{1813}{4}]$ |
$y^2 = x^5 - x^4 - 3x^3 + 2x^2 + x$ |
| 62208.h.186624.1 |
62208.h |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{8} \cdot 3^{6} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.240.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.616135\) |
\(10.896440\) |
\(2.201264\) |
$[90,120,3642,3]$ |
$[540,9270,97236,-8356365,186624]$ |
$[246037500,\frac{15643125}{2},\frac{607725}{4}]$ |
$y^2 = x^5 - 2x^4 - 3x^3 + 3x^2 + 3x$ |
| 62208.i.248832.1 |
62208.i |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{5} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.918980\) |
\(1.918980\) |
$[280,1170,92734,128]$ |
$[840,22380,784384,39504540,248832]$ |
$[1680700000,\frac{159923750}{3},\frac{60054400}{27}]$ |
$y^2 + xy = -x^6 + 11x^4 - 20x^3 + 11x^2 - 2x$ |
| 62208.j.373248.1 |
62208.j |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.075998\) |
\(16.676078\) |
\(1.901015\) |
$[72,573,19875,6]$ |
$[432,-5976,-1979136,-222674832,373248]$ |
$[40310784,-1290816,-989568]$ |
$y^2 + y = 2x^6 - 10x^4 - 12x^3 + 6x + 2$ |
| 62208.k.373248.1 |
62208.k |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{9} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.240.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.379027\) |
\(1.264336\) |
$[2,-486,-1296,-6]$ |
$[12,11670,209956,-33417357,-373248]$ |
$[-\frac{2}{3},-\frac{1945}{36},-\frac{52489}{648}]$ |
$y^2 + x^3y = -3x^4 - 3x^3 + 9x^2 + 18x + 8$ |
| 62208.l.373248.1 |
62208.l |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{9} \cdot 3^{6} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.016986\) |
\(13.399834\) |
\(1.365654\) |
$[36,54,828,-192]$ |
$[108,162,-7236,-201933,-373248]$ |
$[-39366,-\frac{2187}{4},\frac{1809}{8}]$ |
$y^2 + (x + 1)y = x^6 + x^3 + 2x^2 + x$ |
| 62208.m.373248.1 |
62208.m |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{9} \cdot 3^{6} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.095539\) |
\(10.635009\) |
\(1.016060\) |
$[30,78,504,-6]$ |
$[180,-522,10332,396819,-373248]$ |
$[-506250,\frac{32625}{4},-\frac{7175}{8}]$ |
$y^2 + y = 2x^5 + 3x^4 + x^3 + 2x^2$ |
| 62208.n.746496.1 |
62208.n |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(8.616344\) |
\(1.436057\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 = x^6 - 3x^3 + 2$ |
| 62208.o.995328.1 |
62208.o |
\( 2^{8} \cdot 3^{5} \) |
\( - 2^{12} \cdot 3^{5} \) |
$1$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 2^{3} \) |
\(0.146731\) |
\(4.751619\) |
\(2.788839\) |
$[596,414,79842,512]$ |
$[1788,130722,12549308,1337480355,995328]$ |
$[\frac{73439775749}{4},\frac{72070284863}{96},\frac{69651796727}{1728}]$ |
$y^2 + (x + 1)y = -3x^6 - 6x^4 + x^3 - 4x^2 - 1$ |
| 62208.p.995328.1 |
62208.p |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{12} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.189356\) |
\(9.077779\) |
\(1.718935\) |
$[604,810,160350,512]$ |
$[1812,131946,12369604,1250993883,995328]$ |
$[\frac{78502725751}{4},\frac{75713935441}{96},\frac{70509835201}{1728}]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 - x^2 + 9x - 3$ |
