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 |
1089.a1 |
1089k1 |
1089.a |
1089k |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.177816633$ |
$1$ |
|
$8$ |
$288$ |
$-0.087104$ |
$45056/27$ |
$1.13667$ |
$3.16074$ |
$[0, 0, 1, 33, -14]$ |
\(y^2+y=x^3+33x-14\) |
6.2.0.a.1 |
$[(4, 13)]$ |
1089.b1 |
1089j3 |
1089.b |
1089j |
$3$ |
$25$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.2 |
5B.4.2 |
$1650$ |
$1200$ |
$37$ |
$7.655751664$ |
$1$ |
|
$0$ |
$18000$ |
$2.244965$ |
$-52893159101157376/11$ |
$1.09296$ |
$8.50650$ |
$[0, 0, 1, -8516343, -9565943918]$ |
\(y^2+y=x^3-8516343x-9565943918\) |
5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 30.24.0-5.a.2.1, 110.24.1.?, $\ldots$ |
$[(35585/2, 6292843/2)]$ |
1089.b2 |
1089j2 |
1089.b |
1089j |
$3$ |
$25$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.60.0.1 |
5Cs.4.1 |
$1650$ |
$1200$ |
$37$ |
$1.531150332$ |
$1$ |
|
$0$ |
$3600$ |
$1.440245$ |
$-122023936/161051$ |
$1.01300$ |
$5.83251$ |
$[0, 0, 1, -11253, -832208]$ |
\(y^2+y=x^3-11253x-832208\) |
5.60.0.a.1, 22.2.0.a.1, 30.120.0-5.a.1.1, 110.120.5.?, 165.120.0.?, $\ldots$ |
$[(737/2, 14637/2)]$ |
1089.b3 |
1089j1 |
1089.b |
1089j |
$3$ |
$25$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.1 |
5B.4.1 |
$1650$ |
$1200$ |
$37$ |
$0.306230066$ |
$1$ |
|
$6$ |
$720$ |
$0.635525$ |
$-4096/11$ |
$0.82546$ |
$4.43683$ |
$[0, 0, 1, -363, 6322]$ |
\(y^2+y=x^3-363x+6322\) |
5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 30.24.0-5.a.1.1, 110.24.1.?, $\ldots$ |
$[(11, 60)]$ |
1089.c1 |
1089h2 |
1089.c |
1089h |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 11$ |
4.2.0.1, 11.60.1.3 |
11B.10.5 |
$264$ |
$480$ |
$16$ |
$1.460386125$ |
$1$ |
|
$4$ |
$1584$ |
$1.230293$ |
$-24729001$ |
$0.96853$ |
$6.12016$ |
$[1, -1, 1, -32693, -2267130]$ |
\(y^2+xy+y=x^3-x^2-32693x-2267130\) |
4.2.0.a.1, 11.60.1.b.2, 24.4.0-4.a.1.1, 33.120.1-11.b.2.2, 44.120.6.b.2, $\ldots$ |
$[(212, 438)]$ |
1089.c2 |
1089h1 |
1089.c |
1089h |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 11$ |
4.2.0.1, 11.60.1.4 |
11B.10.4 |
$264$ |
$480$ |
$16$ |
$0.132762375$ |
$1$ |
|
$6$ |
$144$ |
$0.031345$ |
$-121$ |
$0.94611$ |
$3.38990$ |
$[1, -1, 1, -23, 168]$ |
\(y^2+xy+y=x^3-x^2-23x+168\) |
4.2.0.a.1, 11.60.1.b.1, 24.4.0-4.a.1.1, 33.120.1-11.b.1.2, 44.120.6.b.1, $\ldots$ |
$[(14, 42)]$ |
1089.d1 |
1089d2 |
1089.d |
1089d |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2880$ |
$1.259563$ |
$19034163/121$ |
$0.94120$ |
$5.86823$ |
$[1, -1, 1, -18173, 942274]$ |
\(y^2+xy+y=x^3-x^2-18173x+942274\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[]$ |
1089.d2 |
1089d1 |
1089.d |
1089d |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1440$ |
$0.912990$ |
$19683/11$ |
$1.13667$ |
$4.88522$ |
$[1, -1, 1, -1838, -5156]$ |
\(y^2+xy+y=x^3-x^2-1838x-5156\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[]$ |
1089.e1 |
1089b1 |
1089.e |
1089b |
$2$ |
$3$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$11$ |
11.165.5.1 |
11Nn.1.4 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$1232$ |
$0.951781$ |
$0$ |
|
$4.96631$ |
$[0, 0, 1, 0, -40263]$ |
\(y^2+y=x^3-40263\) |
|
$[]$ |
1089.e2 |
1089b2 |
1089.e |
1089b |
$2$ |
$3$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$11$ |
11.165.5.1 |
11Nn.1.4 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$3696$ |
$1.501087$ |
$0$ |
|
$5.90892$ |
$[0, 0, 1, 0, 1087094]$ |
\(y^2+y=x^3+1087094\) |
|
$[]$ |
1089.f1 |
1089a2 |
1089.f |
1089a |
$2$ |
$3$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3, 11$ |
27.648.18.4, 11.165.5.1 |
3B.1.2, 11Nn.1.4 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$336$ |
$0.302140$ |
$0$ |
|
$3.85153$ |
$[0, 0, 1, 0, -817]$ |
\(y^2+y=x^3-817\) |
|
$[]$ |
1089.f2 |
1089a1 |
1089.f |
1089a |
$2$ |
$3$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3, 11$ |
27.648.18.1, 11.165.5.1 |
3B.1.1, 11Nn.1.4 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$112$ |
$-0.247166$ |
$0$ |
|
$2.90892$ |
$[0, 0, 1, 0, 30]$ |
\(y^2+y=x^3+30\) |
|
$[]$ |
1089.g1 |
1089e2 |
1089.g |
1089e |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-11})$ |
$-11$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1320$ |
$1.125181$ |
$-32768$ |
$1.02512$ |
$5.52284$ |
$[0, 0, 1, -7986, 281839]$ |
\(y^2+y=x^3-7986x+281839\) |
|
$[]$ |
1089.g2 |
1089e1 |
1089.g |
1089e |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-11})$ |
$-11$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$120$ |
$-0.073767$ |
$-32768$ |
$1.02512$ |
$3.46545$ |
$[0, 0, 1, -66, -212]$ |
\(y^2+y=x^3-66x-212\) |
|
$[]$ |
1089.h1 |
1089c2 |
1089.h |
1089c |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{3} \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$960$ |
$0.710258$ |
$19034163/121$ |
$0.94120$ |
$4.92562$ |
$[1, -1, 0, -2019, -34226]$ |
\(y^2+xy=x^3-x^2-2019x-34226\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[]$ |
1089.h2 |
1089c1 |
1089.h |
1089c |
$2$ |
$2$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{3} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$480$ |
$0.363684$ |
$19683/11$ |
$1.13667$ |
$3.94261$ |
$[1, -1, 0, -204, 259]$ |
\(y^2+xy=x^3-x^2-204x+259\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[]$ |
1089.i1 |
1089f2 |
1089.i |
1089f |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 11$ |
4.2.0.1, 11.60.1.4 |
11B.10.4 |
$264$ |
$480$ |
$16$ |
$5.138097620$ |
$1$ |
|
$2$ |
$1584$ |
$1.230293$ |
$-121$ |
$0.94611$ |
$5.44730$ |
$[1, -1, 0, -2745, -215726]$ |
\(y^2+xy=x^3-x^2-2745x-215726\) |
4.2.0.a.1, 11.60.1.b.1, 33.120.1-11.b.1.1, 44.120.6.b.1, 88.240.16.?, $\ldots$ |
$[(470, 9872)]$ |
1089.i2 |
1089f1 |
1089.i |
1089f |
$2$ |
$11$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{6} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 11$ |
4.2.0.1, 11.60.1.3 |
11B.10.5 |
$264$ |
$480$ |
$16$ |
$0.467099783$ |
$1$ |
|
$2$ |
$144$ |
$0.031345$ |
$-24729001$ |
$0.96853$ |
$4.06277$ |
$[1, -1, 0, -270, 1777]$ |
\(y^2+xy=x^3-x^2-270x+1777\) |
4.2.0.a.1, 11.60.1.b.2, 33.120.1-11.b.2.1, 44.120.6.b.2, 88.240.16.?, $\ldots$ |
$[(8, 5)]$ |
1089.j1 |
1089g3 |
1089.j |
1089g |
$4$ |
$4$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 11^{10} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.14 |
2B |
$264$ |
$48$ |
$0$ |
$2.957701004$ |
$1$ |
|
$2$ |
$5760$ |
$1.735622$ |
$347873904937/395307$ |
$1.00913$ |
$6.80024$ |
$[1, -1, 0, -159561, 24548134]$ |
\(y^2+xy=x^3-x^2-159561x+24548134\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0.h.1, 24.24.0-12.h.1.4, $\ldots$ |
$[(-382, 5636)]$ |
1089.j2 |
1089g2 |
1089.j |
1089g |
$4$ |
$4$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.2 |
2Cs |
$132$ |
$48$ |
$0$ |
$5.915402008$ |
$1$ |
|
$2$ |
$2880$ |
$1.389048$ |
$169112377/88209$ |
$1.00669$ |
$5.70929$ |
$[1, -1, 0, -12546, 173047]$ |
\(y^2+xy=x^3-x^2-12546x+173047\) |
2.6.0.a.1, 4.12.0-2.a.1.2, 12.24.0-12.a.1.4, 44.24.0-44.b.1.4, 132.48.0.? |
$[(5603/2, 412357/2)]$ |
1089.j3 |
1089g1 |
1089.j |
1089g |
$4$ |
$4$ |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 11^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.14 |
2B |
$264$ |
$48$ |
$0$ |
$2.957701004$ |
$1$ |
|
$3$ |
$1440$ |
$1.042475$ |
$30664297/297$ |
$1.09706$ |
$5.46512$ |
$[1, -1, 0, -7101, -226616]$ |
\(y^2+xy=x^3-x^2-7101x-226616\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.13, $\ldots$ |
$[(1400, 51572)]$ |
1089.j4 |
1089g4 |
1089.j |
1089g |
$4$ |
$4$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{18} \cdot 11^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.14 |
2B |
$264$ |
$48$ |
$0$ |
$2.957701004$ |
$1$ |
|
$0$ |
$5760$ |
$1.735622$ |
$9090072503/5845851$ |
$1.03763$ |
$6.27905$ |
$[1, -1, 0, 47349, 1311052]$ |
\(y^2+xy=x^3-x^2+47349x+1311052\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0-4.c.1.1, 22.6.0.a.1, $\ldots$ |
$[(419/2, 21361/2)]$ |
1089.k1 |
1089i1 |
1089.k |
1089i |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \) |
\( - 3^{9} \cdot 11^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.677917086$ |
$1$ |
|
$0$ |
$3168$ |
$1.111843$ |
$45056/27$ |
$1.13667$ |
$5.21814$ |
$[0, 0, 1, 3993, 18301]$ |
\(y^2+y=x^3+3993x+18301\) |
6.2.0.a.1 |
$[(121/2, 3263/2)]$ |