| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 27.a1 |
27a2 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.13.34 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$3$ |
$0.052148$ |
$-12288000$ |
$1.23864$ |
$8.61966$ |
$[0, 0, 1, -270, -1708]$ |
\(y^2+y=x^3-270x-1708\) |
|
$[ ]$ |
| 27.a2 |
27a4 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{5} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.13.25 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$9$ |
$-0.497158$ |
$-12288000$ |
$1.23864$ |
$6.61966$ |
$[0, 0, 1, -30, 63]$ |
\(y^2+y=x^3-30x+63\) |
|
$[ ]$ |
| 432.e1 |
432a4 |
432.e |
432a |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$216$ |
$0.745296$ |
$-12288000$ |
$1.23864$ |
$6.05211$ |
$[0, 0, 0, -4320, 109296]$ |
\(y^2=x^3-4320x+109296\) |
|
$[ ]$ |
| 432.e2 |
432a2 |
432.e |
432a |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$72$ |
$0.195989$ |
$-12288000$ |
$1.23864$ |
$4.96588$ |
$[0, 0, 0, -480, -4048]$ |
\(y^2=x^3-480x-4048\) |
|
$[ ]$ |
| 675.e1 |
675a4 |
675.e |
675a |
$4$ |
$27$ |
\( 3^{3} \cdot 5^{2} \) |
\( - 3^{11} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.650319782$ |
$1$ |
|
$2$ |
$432$ |
$0.856867$ |
$-12288000$ |
$1.23864$ |
$5.84303$ |
$[0, 0, 1, -6750, -213469]$ |
\(y^2+y=x^3-6750x-213469\) |
|
$[(145, 1362)]$ |
| 675.e2 |
675a3 |
675.e |
675a |
$4$ |
$27$ |
\( 3^{3} \cdot 5^{2} \) |
\( - 3^{5} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.135197028$ |
$1$ |
|
$8$ |
$144$ |
$0.307561$ |
$-12288000$ |
$1.23864$ |
$4.83121$ |
$[0, 0, 1, -750, 7906]$ |
\(y^2+y=x^3-750x+7906\) |
|
$[(10, 37)]$ |
| 1323.i1 |
1323b4 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{11} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1134$ |
$1.025103$ |
$-12288000$ |
$1.23864$ |
$5.57685$ |
$[0, 0, 1, -13230, 585758]$ |
\(y^2+y=x^3-13230x+585758\) |
|
$[ ]$ |
| 1323.i2 |
1323b2 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$378$ |
$0.475797$ |
$-12288000$ |
$1.23864$ |
$4.65977$ |
$[0, 0, 1, -1470, -21695]$ |
\(y^2+y=x^3-1470x-21695\) |
|
$[ ]$ |
| 1728.n1 |
1728a4 |
1728.n |
1728a |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$6.791192128$ |
$1$ |
|
$2$ |
$432$ |
$0.398722$ |
$-12288000$ |
$1.23864$ |
$4.36876$ |
$[0, 0, 0, -1080, -13662]$ |
\(y^2=x^3-1080x-13662\) |
|
$[(871, 25687)]$ |
| 1728.n2 |
1728a3 |
1728.n |
1728a |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.251525634$ |
$1$ |
|
$4$ |
$144$ |
$-0.150585$ |
$-12288000$ |
$1.23864$ |
$3.48453$ |
$[0, 0, 0, -120, 506]$ |
\(y^2=x^3-120x+506\) |
|
$[(7, 3)]$ |
| 1728.o1 |
1728v4 |
1728.o |
1728v |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.349576835$ |
$1$ |
|
$2$ |
$432$ |
$0.398722$ |
$-12288000$ |
$1.23864$ |
$4.36876$ |
$[0, 0, 0, -1080, 13662]$ |
\(y^2=x^3-1080x+13662\) |
|
$[(19, 1)]$ |
| 1728.o2 |
1728v2 |
1728.o |
1728v |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.048730507$ |
$1$ |
|
$2$ |
$144$ |
$-0.150585$ |
$-12288000$ |
$1.23864$ |
$3.48453$ |
$[0, 0, 0, -120, -506]$ |
\(y^2=x^3-120x-506\) |
|
$[(51, 355)]$ |
| 3267.f1 |
3267d4 |
3267.f |
3267d |
$4$ |
$27$ |
\( 3^{3} \cdot 11^{2} \) |
\( - 3^{11} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.571787496$ |
$1$ |
|
$2$ |
$4320$ |
$1.251095$ |
$-12288000$ |
$1.23864$ |
$5.28897$ |
$[0, 0, 1, -32670, 2273015]$ |
\(y^2+y=x^3-32670x+2273015\) |
|
$[(121, 302)]$ |
| 3267.f2 |
3267d2 |
3267.f |
3267d |
$4$ |
$27$ |
\( 3^{3} \cdot 11^{2} \) |
\( - 3^{5} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.715362490$ |
$1$ |
|
$0$ |
$1440$ |
$0.701790$ |
$-12288000$ |
$1.23864$ |
$4.47434$ |
$[0, 0, 1, -3630, -84186]$ |
\(y^2+y=x^3-3630x-84186\) |
|
$[(1089/2, 34965/2)]$ |
| 4563.e1 |
4563g4 |
4563.e |
4563g |
$4$ |
$27$ |
\( 3^{3} \cdot 13^{2} \) |
\( - 3^{11} \cdot 13^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$9$ |
$3$ |
$0$ |
$6156$ |
$1.334623$ |
$-12288000$ |
$1.23864$ |
$5.19821$ |
$[0, 0, 1, -45630, -3751927]$ |
\(y^2+y=x^3-45630x-3751927\) |
|
$[ ]$ |
| 4563.e2 |
4563g3 |
4563.e |
4563g |
$4$ |
$27$ |
\( 3^{3} \cdot 13^{2} \) |
\( - 3^{5} \cdot 13^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$2052$ |
$0.785316$ |
$-12288000$ |
$1.23864$ |
$4.41588$ |
$[0, 0, 1, -5070, 138960]$ |
\(y^2+y=x^3-5070x+138960\) |
|
$[ ]$ |
| 7803.k1 |
7803a4 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{11} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$12.73716166$ |
$1$ |
|
$0$ |
$15552$ |
$1.468754$ |
$-12288000$ |
$1.23864$ |
$5.06661$ |
$[0, 0, 1, -78030, -8390176]$ |
\(y^2+y=x^3-78030x-8390176\) |
|
$[(3970537/106, 3402396543/106)]$ |
| 7803.k2 |
7803a3 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{5} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.471746728$ |
$1$ |
|
$4$ |
$5184$ |
$0.919449$ |
$-12288000$ |
$1.23864$ |
$4.33112$ |
$[0, 0, 1, -8670, 310747]$ |
\(y^2+y=x^3-8670x+310747\) |
|
$[(85, 433)]$ |
| 9747.f1 |
9747a4 |
9747.f |
9747a |
$4$ |
$27$ |
\( 3^{3} \cdot 19^{2} \) |
\( - 3^{11} \cdot 19^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$18954$ |
$1.524368$ |
$-12288000$ |
$1.23864$ |
$5.01656$ |
$[0, 0, 1, -97470, 11713457]$ |
\(y^2+y=x^3-97470x+11713457\) |
|
$[ ]$ |
| 9747.f2 |
9747a2 |
9747.f |
9747a |
$4$ |
$27$ |
\( 3^{3} \cdot 19^{2} \) |
\( - 3^{5} \cdot 19^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$6318$ |
$0.975061$ |
$-12288000$ |
$1.23864$ |
$4.29888$ |
$[0, 0, 1, -10830, -433832]$ |
\(y^2+y=x^3-10830x-433832\) |
|
$[ ]$ |
| 10800.bo1 |
10800cz4 |
10800.bo |
10800cz |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{11} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.118107923$ |
$1$ |
|
$2$ |
$31104$ |
$1.550014$ |
$-12288000$ |
$1.23864$ |
$4.99428$ |
$[0, 0, 0, -108000, 13662000]$ |
\(y^2=x^3-108000x+13662000\) |
|
$[(145, 1025)]$ |
| 10800.bo2 |
10800cz2 |
10800.bo |
10800cz |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$9.354323771$ |
$1$ |
|
$0$ |
$10368$ |
$1.000708$ |
$-12288000$ |
$1.23864$ |
$4.28453$ |
$[0, 0, 0, -12000, -506000]$ |
\(y^2=x^3-12000x-506000\) |
|
$[(39465/17, 3114275/17)]$ |
| 14283.g1 |
14283i4 |
14283.g |
14283i |
$4$ |
$27$ |
\( 3^{3} \cdot 23^{2} \) |
\( - 3^{11} \cdot 23^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.391021540$ |
$1$ |
|
$0$ |
$38016$ |
$1.619896$ |
$-12288000$ |
$1.23864$ |
$4.93601$ |
$[0, 0, 1, -142830, 20778194]$ |
\(y^2+y=x^3-142830x+20778194\) |
|
$[(529/2, 16395/2)]$ |
| 14283.g2 |
14283i2 |
14283.g |
14283i |
$4$ |
$27$ |
\( 3^{3} \cdot 23^{2} \) |
\( - 3^{5} \cdot 23^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$10.17306462$ |
$1$ |
|
$0$ |
$12672$ |
$1.070589$ |
$-12288000$ |
$1.23864$ |
$4.24700$ |
$[0, 0, 1, -15870, -769563]$ |
\(y^2+y=x^3-15870x-769563\) |
|
$[(413149/51, 112284017/51)]$ |
| 21168.bv1 |
21168cx4 |
21168.bv |
21168cx |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{11} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$9$ |
$3$ |
$0$ |
$81648$ |
$1.718250$ |
$-12288000$ |
$1.23864$ |
$4.85954$ |
$[0, 0, 0, -211680, -37488528]$ |
\(y^2=x^3-211680x-37488528\) |
|
$[ ]$ |
| 21168.bv2 |
21168cx3 |
21168.bv |
21168cx |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$27216$ |
$1.168943$ |
$-12288000$ |
$1.23864$ |
$4.19774$ |
$[0, 0, 0, -23520, 1388464]$ |
\(y^2=x^3-23520x+1388464\) |
|
$[ ]$ |
| 22707.c1 |
22707a4 |
22707.c |
22707a |
$4$ |
$27$ |
\( 3^{3} \cdot 29^{2} \) |
\( - 3^{11} \cdot 29^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$19.81400594$ |
$1$ |
|
$0$ |
$75600$ |
$1.735796$ |
$-12288000$ |
$1.23864$ |
$4.84653$ |
$[0, 0, 1, -227070, -41650315]$ |
\(y^2+y=x^3-227070x-41650315\) |
|
$[(10465089379/2103, 1046911976256014/2103)]$ |
| 22707.c2 |
22707a3 |
22707.c |
22707a |
$4$ |
$27$ |
\( 3^{3} \cdot 29^{2} \) |
\( - 3^{5} \cdot 29^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.733852072$ |
$1$ |
|
$4$ |
$25200$ |
$1.186489$ |
$-12288000$ |
$1.23864$ |
$4.18936$ |
$[0, 0, 1, -25230, 1542604]$ |
\(y^2+y=x^3-25230x+1542604\) |
|
$[(116, 420)]$ |
| 25947.c1 |
25947b4 |
25947.c |
25947b |
$4$ |
$27$ |
\( 3^{3} \cdot 31^{2} \) |
\( - 3^{11} \cdot 31^{6} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.009274303$ |
$1$ |
|
$6$ |
$90720$ |
$1.769142$ |
$-12288000$ |
$1.23864$ |
$4.82230$ |
$[0, 0, 1, -259470, 50875580]$ |
\(y^2+y=x^3-259470x+50875580\) |
|
$[(310, 480), (-62, 8168)]$ |
| 25947.c2 |
25947b2 |
25947.c |
25947b |
$4$ |
$27$ |
\( 3^{3} \cdot 31^{2} \) |
\( - 3^{5} \cdot 31^{6} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.009274303$ |
$1$ |
|
$8$ |
$30240$ |
$1.219835$ |
$-12288000$ |
$1.23864$ |
$4.17376$ |
$[0, 0, 1, -28830, -1884281]$ |
\(y^2+y=x^3-28830x-1884281\) |
|
$[(217, 1441), (403, 7207)]$ |
| 33075.bn1 |
33075bn4 |
33075.bn |
33075bn |
$4$ |
$27$ |
\( 3^{3} \cdot 5^{2} \cdot 7^{2} \) |
\( - 3^{11} \cdot 5^{6} \cdot 7^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.854482209$ |
$1$ |
|
$0$ |
$163296$ |
$1.829823$ |
$-12288000$ |
$1.23864$ |
$4.77980$ |
$[0, 0, 1, -330750, 73219781]$ |
\(y^2+y=x^3-330750x+73219781\) |
|
$[(2965/3, 2924/3)]$ |
| 33075.bn2 |
33075bn2 |
33075.bn |
33075bn |
$4$ |
$27$ |
\( 3^{3} \cdot 5^{2} \cdot 7^{2} \) |
\( - 3^{5} \cdot 5^{6} \cdot 7^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$14.56344662$ |
$1$ |
|
$0$ |
$54432$ |
$1.280516$ |
$-12288000$ |
$1.23864$ |
$4.14638$ |
$[0, 0, 1, -36750, -2711844]$ |
\(y^2+y=x^3-36750x-2711844\) |
|
$[(7056345/178, 2180919249/178)]$ |
| 36963.h1 |
36963e4 |
36963.h |
36963e |
$4$ |
$27$ |
\( 3^{3} \cdot 37^{2} \) |
\( - 3^{11} \cdot 37^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$9$ |
$3$ |
$0$ |
$142884$ |
$1.857607$ |
$-12288000$ |
$1.23864$ |
$4.76099$ |
$[0, 0, 1, -369630, -86502661]$ |
\(y^2+y=x^3-369630x-86502661\) |
|
$[ ]$ |
| 36963.h2 |
36963e3 |
36963.h |
36963e |
$4$ |
$27$ |
\( 3^{3} \cdot 37^{2} \) |
\( - 3^{5} \cdot 37^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$47628$ |
$1.308300$ |
$-12288000$ |
$1.23864$ |
$4.13426$ |
$[0, 0, 1, -41070, 3203802]$ |
\(y^2+y=x^3-41070x+3203802\) |
|
$[ ]$ |
| 43200.eg1 |
43200fk4 |
43200.eg |
43200fk |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{11} \cdot 5^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$62208$ |
$1.203440$ |
$-12288000$ |
$1.23864$ |
$3.95598$ |
$[0, 0, 0, -27000, 1707750]$ |
\(y^2=x^3-27000x+1707750\) |
|
$[ ]$ |
| 43200.eg2 |
43200fk2 |
43200.eg |
43200fk |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{5} \cdot 5^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$20736$ |
$0.654135$ |
$-12288000$ |
$1.23864$ |
$3.33841$ |
$[0, 0, 0, -3000, -63250]$ |
\(y^2=x^3-3000x-63250\) |
|
$[ ]$ |
| 43200.gl1 |
43200ct4 |
43200.gl |
43200ct |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{11} \cdot 5^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$9$ |
$3$ |
$0$ |
$62208$ |
$1.203440$ |
$-12288000$ |
$1.23864$ |
$3.95598$ |
$[0, 0, 0, -27000, -1707750]$ |
\(y^2=x^3-27000x-1707750\) |
|
$[ ]$ |
| 43200.gl2 |
43200ct3 |
43200.gl |
43200ct |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{5} \cdot 5^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$20736$ |
$0.654135$ |
$-12288000$ |
$1.23864$ |
$3.33841$ |
$[0, 0, 0, -3000, 63250]$ |
\(y^2=x^3-3000x+63250\) |
|
$[ ]$ |
| 45387.e1 |
45387a4 |
45387.e |
45387a |
$4$ |
$27$ |
\( 3^{3} \cdot 41^{2} \) |
\( - 3^{11} \cdot 41^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$24.96764822$ |
$1$ |
|
$0$ |
$211680$ |
$1.908934$ |
$-12288000$ |
$1.23864$ |
$4.72727$ |
$[0, 0, 1, -453870, -117699838]$ |
\(y^2+y=x^3-453870x-117699838\) |
|
$[(2756190808009/16196, 4566117353311412187/16196)]$ |
| 45387.e2 |
45387a3 |
45387.e |
45387a |
$4$ |
$27$ |
\( 3^{3} \cdot 41^{2} \) |
\( - 3^{5} \cdot 41^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.924727711$ |
$1$ |
|
$4$ |
$70560$ |
$1.359629$ |
$-12288000$ |
$1.23864$ |
$4.11255$ |
$[0, 0, 1, -50430, 4359253]$ |
\(y^2+y=x^3-50430x+4359253\) |
|
$[(-41, 2521)]$ |
| 49923.g1 |
49923d4 |
49923.g |
49923d |
$4$ |
$27$ |
\( 3^{3} \cdot 43^{2} \) |
\( - 3^{11} \cdot 43^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$235872$ |
$1.932749$ |
$-12288000$ |
$1.23864$ |
$4.71206$ |
$[0, 0, 1, -499230, 135778079]$ |
\(y^2+y=x^3-499230x+135778079\) |
|
$[ ]$ |
| 49923.g2 |
49923d2 |
49923.g |
49923d |
$4$ |
$27$ |
\( 3^{3} \cdot 43^{2} \) |
\( - 3^{5} \cdot 43^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$78624$ |
$1.383442$ |
$-12288000$ |
$1.23864$ |
$4.10275$ |
$[0, 0, 1, -55470, -5028818]$ |
\(y^2+y=x^3-55470x-5028818\) |
|
$[ ]$ |
| 52272.bk1 |
52272bj4 |
52272.bk |
52272bj |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{11} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$27.23659680$ |
$1$ |
|
$0$ |
$311040$ |
$1.944242$ |
$-12288000$ |
$1.23864$ |
$4.70482$ |
$[0, 0, 0, -522720, -145472976]$ |
\(y^2=x^3-522720x-145472976\) |
|
$[(6403117707481/49229, 15517679956898097275/49229)]$ |
| 52272.bk2 |
52272bj2 |
52272.bk |
52272bj |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 11^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.008762844$ |
$1$ |
|
$2$ |
$103680$ |
$1.394938$ |
$-12288000$ |
$1.23864$ |
$4.09808$ |
$[0, 0, 0, -58080, 5387888]$ |
\(y^2=x^3-58080x+5387888\) |
|
$[(121, 363)]$ |
| 59643.f1 |
59643d4 |
59643.f |
59643d |
$4$ |
$27$ |
\( 3^{3} \cdot 47^{2} \) |
\( - 3^{11} \cdot 47^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.692411943$ |
$1$ |
|
$0$ |
$317952$ |
$1.977222$ |
$-12288000$ |
$1.23864$ |
$4.68436$ |
$[0, 0, 1, -596430, 177303728]$ |
\(y^2+y=x^3-596430x+177303728\) |
|
$[(16873/6, 183239/6)]$ |
| 59643.f2 |
59643d2 |
59643.f |
59643d |
$4$ |
$27$ |
\( 3^{3} \cdot 47^{2} \) |
\( - 3^{5} \cdot 47^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$14.07723582$ |
$1$ |
|
$0$ |
$105984$ |
$1.427916$ |
$-12288000$ |
$1.23864$ |
$4.08491$ |
$[0, 0, 1, -66270, -6566805]$ |
\(y^2+y=x^3-66270x-6566805\) |
|
$[(40713609/370, 8436585977/370)]$ |
| 73008.bs1 |
73008bi4 |
73008.bs |
73008bi |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 13^{2} \) |
\( - 2^{12} \cdot 3^{11} \cdot 13^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$443232$ |
$2.027771$ |
$-12288000$ |
$1.23864$ |
$4.65395$ |
$[0, 0, 0, -730080, 240123312]$ |
\(y^2=x^3-730080x+240123312\) |
|
$[ ]$ |
| 73008.bs2 |
73008bi2 |
73008.bs |
73008bi |
$4$ |
$27$ |
\( 2^{4} \cdot 3^{3} \cdot 13^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 13^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$147744$ |
$1.478464$ |
$-12288000$ |
$1.23864$ |
$4.06532$ |
$[0, 0, 0, -81120, -8893456]$ |
\(y^2=x^3-81120x-8893456\) |
|
$[ ]$ |
| 75843.d1 |
75843a4 |
75843.d |
75843a |
$4$ |
$27$ |
\( 3^{3} \cdot 53^{2} \) |
\( - 3^{11} \cdot 53^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$35.33187899$ |
$1$ |
|
$0$ |
$454896$ |
$2.037292$ |
$-12288000$ |
$1.23864$ |
$4.64835$ |
$[0, 0, 1, -758430, -254244697]$ |
\(y^2+y=x^3-758430x-254244697\) |
|
$[(82000819327229611/8360107, 12679952231729444552206968/8360107)]$ |
| 75843.d2 |
75843a2 |
75843.d |
75843a |
$4$ |
$27$ |
\( 3^{3} \cdot 53^{2} \) |
\( - 3^{5} \cdot 53^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.308588111$ |
$1$ |
|
$4$ |
$151632$ |
$1.487988$ |
$-12288000$ |
$1.23864$ |
$4.06171$ |
$[0, 0, 1, -84270, 9416470]$ |
\(y^2+y=x^3-84270x+9416470\) |
|
$[(-212, 4213)]$ |
