| 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 |
| 1728.a1 |
1728l1 |
1728.a |
1728l |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.528284$ |
$-3072$ |
$0.94639$ |
$4.05987$ |
$[0, 0, 0, -432, -4320]$ |
\(y^2=x^3-432x-4320\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[]$ |
| 1728.b1 |
1728u1 |
1728.b |
1728u |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.528284$ |
$-3072$ |
$0.94639$ |
$4.05987$ |
$[0, 0, 0, -432, 4320]$ |
\(y^2=x^3-432x+4320\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[]$ |
| 1728.c1 |
1728e3 |
1728.c |
1728e |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{27} \cdot 3^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.4 |
3B |
$72$ |
$144$ |
$3$ |
$2.543458324$ |
$1$ |
|
$2$ |
$3456$ |
$1.273823$ |
$-1167051/512$ |
$1.04966$ |
$5.24441$ |
$[0, 0, 0, -7884, -357264]$ |
\(y^2=x^3-7884x-357264\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.36.0.d.1, 18.72.0-9.d.1.1, 24.16.0-24.d.1.2, $\ldots$ |
$[(430, 8704)]$ |
| 1728.c2 |
1728e1 |
1728.c |
1728e |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{19} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.5 |
3B |
$72$ |
$144$ |
$3$ |
$0.282606480$ |
$1$ |
|
$4$ |
$384$ |
$0.175210$ |
$-132651/2$ |
$1.09453$ |
$3.70150$ |
$[0, 0, 0, -204, 1136]$ |
\(y^2=x^3-204x+1136\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.36.0.d.2, 18.72.0-9.d.2.2, 24.16.0-24.d.1.1, $\ldots$ |
$[(14, 32)]$ |
| 1728.c3 |
1728e2 |
1728.c |
1728e |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{21} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.1 |
3Cs |
$72$ |
$144$ |
$3$ |
$0.847819441$ |
$1$ |
|
$4$ |
$1152$ |
$0.724516$ |
$9261/8$ |
$1.19875$ |
$4.22521$ |
$[0, 0, 0, 756, 5616]$ |
\(y^2=x^3+756x+5616\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 9.36.0.a.1, 18.72.0-9.a.1.2, 24.48.1-24.ci.1.3, $\ldots$ |
$[(-2, 64)]$ |
| 1728.d1 |
1728bb3 |
1728.d |
1728bb |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{27} \cdot 3^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.4 |
3B |
$72$ |
$144$ |
$3$ |
$1.015681695$ |
$1$ |
|
$4$ |
$3456$ |
$1.273823$ |
$-1167051/512$ |
$1.04966$ |
$5.24441$ |
$[0, 0, 0, -7884, 357264]$ |
\(y^2=x^3-7884x+357264\) |
3.4.0.a.1, 9.36.0.d.1, 12.8.0-3.a.1.3, 24.16.0-24.d.1.5, 36.72.0-9.d.1.3, $\ldots$ |
$[(82, 512)]$ |
| 1728.d2 |
1728bb1 |
1728.d |
1728bb |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{19} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.5 |
3B |
$72$ |
$144$ |
$3$ |
$1.015681695$ |
$1$ |
|
$4$ |
$384$ |
$0.175210$ |
$-132651/2$ |
$1.09453$ |
$3.70150$ |
$[0, 0, 0, -204, -1136]$ |
\(y^2=x^3-204x-1136\) |
3.4.0.a.1, 9.36.0.d.2, 12.8.0-3.a.1.4, 24.16.0-24.d.1.6, 36.72.0-9.d.2.3, $\ldots$ |
$[(18, 32)]$ |
| 1728.d3 |
1728bb2 |
1728.d |
1728bb |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{21} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.1 |
3Cs |
$72$ |
$144$ |
$3$ |
$0.338560565$ |
$1$ |
|
$4$ |
$1152$ |
$0.724516$ |
$9261/8$ |
$1.19875$ |
$4.22521$ |
$[0, 0, 0, 756, -5616]$ |
\(y^2=x^3+756x-5616\) |
3.12.0.a.1, 9.36.0.a.1, 12.24.0-3.a.1.2, 24.48.1-24.ci.1.2, 36.72.0-9.a.1.3, $\ldots$ |
$[(66, 576)]$ |
| 1728.e1 |
1728ba1 |
1728.e |
1728ba |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$24$ |
$24$ |
$1$ |
$0.555032222$ |
$1$ |
|
$2$ |
$96$ |
$-0.629178$ |
$-13824$ |
$1.22629$ |
$2.29474$ |
$[0, 0, 0, -6, 6]$ |
\(y^2=x^3-6x+6\) |
3.3.0.a.1, 6.6.1.b.1, 12.12.1.g.1, 24.24.1-12.g.1.1 |
$[(1, 1)]$ |
| 1728.f1 |
1728d1 |
1728.f |
1728d |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$2.021940563$ |
$1$ |
|
$2$ |
$288$ |
$0.042505$ |
$1536$ |
$1.22629$ |
$3.16317$ |
$[0, 0, 0, 54, -54]$ |
\(y^2=x^3+54x-54\) |
6.2.0.a.1 |
$[(1, 1)]$ |
| 1728.g1 |
1728i1 |
1728.g |
1728i |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.042505$ |
$1536$ |
$1.22629$ |
$3.16317$ |
$[0, 0, 0, 54, 54]$ |
\(y^2=x^3+54x+54\) |
6.2.0.a.1 |
$[]$ |
| 1728.h1 |
1728r1 |
1728.h |
1728r |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$24$ |
$24$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$-0.629178$ |
$-13824$ |
$1.22629$ |
$2.29474$ |
$[0, 0, 0, -6, -6]$ |
\(y^2=x^3-6x-6\) |
3.3.0.a.1, 6.6.1.b.1, 12.12.1.g.1, 24.24.1-12.g.1.1 |
$[]$ |
| 1728.i1 |
1728p1 |
1728.i |
1728p |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{17} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.668368$ |
$-6$ |
$1.22518$ |
$4.20223$ |
$[0, 0, 0, -108, -7344]$ |
\(y^2=x^3-108x-7344\) |
24.2.0.b.1 |
$[]$ |
| 1728.j1 |
1728o1 |
1728.j |
1728o |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{15} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.375104$ |
$-216$ |
$1.22629$ |
$3.73686$ |
$[0, 0, 0, -108, -1296]$ |
\(y^2=x^3-108x-1296\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[]$ |
| 1728.k1 |
1728y1 |
1728.k |
1728y |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{15} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$0.170724129$ |
$1$ |
|
$8$ |
$576$ |
$0.375104$ |
$-216$ |
$1.22629$ |
$3.73686$ |
$[0, 0, 0, -108, 1296]$ |
\(y^2=x^3-108x+1296\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[(18, 72)]$ |
| 1728.l1 |
1728g1 |
1728.l |
1728g |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{17} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.668368$ |
$-6$ |
$1.22518$ |
$4.20223$ |
$[0, 0, 0, -108, 7344]$ |
\(y^2=x^3-108x+7344\) |
24.2.0.b.1 |
$[]$ |
| 1728.m1 |
1728m1 |
1728.m |
1728m |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.237793$ |
$0$ |
|
$2.74385$ |
$[0, 0, 0, 0, -32]$ |
\(y^2=x^3-32\) |
|
$[]$ |
| 1728.m2 |
1728m2 |
1728.m |
1728m |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.311513$ |
$0$ |
|
$3.62808$ |
$[0, 0, 0, 0, 864]$ |
\(y^2=x^3+864\) |
|
$[]$ |
| 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.n3 |
1728a2 |
1728.n |
1728a |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$2.263730709$ |
$1$ |
|
$2$ |
$144$ |
$-0.150585$ |
$0$ |
|
$2.88423$ |
$[0, 0, 0, 0, -54]$ |
\(y^2=x^3-54\) |
|
$[(7, 17)]$ |
| 1728.n4 |
1728a1 |
1728.n |
1728a |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$0.754576903$ |
$1$ |
|
$2$ |
$48$ |
$-0.699891$ |
$0$ |
|
$2.00000$ |
$[0, 0, 0, 0, 2]$ |
\(y^2=x^3+2\) |
|
$[(-1, 1)]$ |
| 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 |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.048730507$ |
$1$ |
|
$2$ |
$144$ |
$-0.150585$ |
$-12288000$ |
$1.23864$ |
$3.48453$ |
$[0, 0, 0, -120, -506]$ |
\(y^2=x^3-120x-506\) |
|
$[(51, 355)]$ |
| 1728.o3 |
1728v1 |
1728.o |
1728v |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$1.349576835$ |
$1$ |
|
$2$ |
$48$ |
$-0.699891$ |
$0$ |
|
$2.00000$ |
$[0, 0, 0, 0, -2]$ |
\(y^2=x^3-2\) |
|
$[(3, 5)]$ |
| 1728.o4 |
1728v3 |
1728.o |
1728v |
$4$ |
$27$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$0.449858945$ |
$1$ |
|
$2$ |
$144$ |
$-0.150585$ |
$0$ |
|
$2.88423$ |
$[0, 0, 0, 0, 54]$ |
\(y^2=x^3+54\) |
|
$[(3, 9)]$ |
| 1728.p1 |
1728f2 |
1728.p |
1728f |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.311513$ |
$0$ |
|
$3.62808$ |
$[0, 0, 0, 0, -864]$ |
\(y^2=x^3-864\) |
|
$[]$ |
| 1728.p2 |
1728f1 |
1728.p |
1728f |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.237793$ |
$0$ |
|
$2.74385$ |
$[0, 0, 0, 0, 32]$ |
\(y^2=x^3+32\) |
|
$[]$ |
| 1728.q1 |
1728w1 |
1728.q |
1728w |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{15} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$0.292341859$ |
$1$ |
|
$4$ |
$192$ |
$-0.174202$ |
$-216$ |
$1.22629$ |
$2.85263$ |
$[0, 0, 0, -12, 48]$ |
\(y^2=x^3-12x+48\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[(-2, 8)]$ |
| 1728.r1 |
1728x1 |
1728.r |
1728x |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{17} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$0.425874033$ |
$1$ |
|
$4$ |
$384$ |
$0.119062$ |
$-6$ |
$1.22518$ |
$3.31800$ |
$[0, 0, 0, -12, 272]$ |
\(y^2=x^3-12x+272\) |
24.2.0.b.1 |
$[(2, 16)]$ |
| 1728.s1 |
1728b1 |
1728.s |
1728b |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{17} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$0.278107440$ |
$1$ |
|
$6$ |
$384$ |
$0.119062$ |
$-6$ |
$1.22518$ |
$3.31800$ |
$[0, 0, 0, -12, -272]$ |
\(y^2=x^3-12x-272\) |
24.2.0.b.1 |
$[(14, 48)]$ |
| 1728.t1 |
1728n1 |
1728.t |
1728n |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{15} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.174202$ |
$-216$ |
$1.22629$ |
$2.85263$ |
$[0, 0, 0, -12, -48]$ |
\(y^2=x^3-12x-48\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[]$ |
| 1728.u1 |
1728z1 |
1728.u |
1728z |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$24$ |
$24$ |
$1$ |
$1.122850992$ |
$1$ |
|
$2$ |
$288$ |
$-0.079872$ |
$-13824$ |
$1.22629$ |
$3.17897$ |
$[0, 0, 0, -54, -162]$ |
\(y^2=x^3-54x-162\) |
3.3.0.a.1, 6.6.1.b.1, 12.12.1.g.1, 24.24.1-12.g.1.1 |
$[(9, 9)]$ |
| 1728.v1 |
1728c1 |
1728.v |
1728c |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$0.415853478$ |
$1$ |
|
$4$ |
$96$ |
$-0.506801$ |
$1536$ |
$1.22629$ |
$2.27894$ |
$[0, 0, 0, 6, 2]$ |
\(y^2=x^3+6x+2\) |
6.2.0.a.1 |
$[(1, 3)]$ |
| 1728.w1 |
1728h1 |
1728.w |
1728h |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$-0.506801$ |
$1536$ |
$1.22629$ |
$2.27894$ |
$[0, 0, 0, 6, -2]$ |
\(y^2=x^3+6x-2\) |
6.2.0.a.1 |
$[]$ |
| 1728.x1 |
1728q1 |
1728.x |
1728q |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$24$ |
$24$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$-0.079872$ |
$-13824$ |
$1.22629$ |
$3.17897$ |
$[0, 0, 0, -54, 162]$ |
\(y^2=x^3-54x+162\) |
3.3.0.a.1, 6.6.1.b.1, 12.12.1.g.1, 24.24.1-12.g.1.1 |
$[]$ |
| 1728.y1 |
1728j2 |
1728.y |
1728j |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{19} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.5 |
3B |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.724516$ |
$-132651/2$ |
$1.09453$ |
$4.58573$ |
$[0, 0, 0, -1836, -30672]$ |
\(y^2=x^3-1836x-30672\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.36.0.d.2, 18.72.0-9.d.2.1, 24.16.0-24.d.1.2, $\ldots$ |
$[]$ |
| 1728.y2 |
1728j3 |
1728.y |
1728j |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{27} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.4 |
3B |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.724516$ |
$-1167051/512$ |
$1.04966$ |
$4.36018$ |
$[0, 0, 0, -876, 13232]$ |
\(y^2=x^3-876x+13232\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.36.0.d.1, 18.72.0-9.d.1.2, 24.16.0-24.d.1.1, $\ldots$ |
$[]$ |
| 1728.y3 |
1728j1 |
1728.y |
1728j |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{21} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.1 |
3Cs |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.175210$ |
$9261/8$ |
$1.19875$ |
$3.34098$ |
$[0, 0, 0, 84, -208]$ |
\(y^2=x^3+84x-208\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 9.36.0.a.1, 18.72.0-9.a.1.1, 24.48.1-24.ci.1.3, $\ldots$ |
$[]$ |
| 1728.z1 |
1728s3 |
1728.z |
1728s |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{19} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.5 |
3B |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.724516$ |
$-132651/2$ |
$1.09453$ |
$4.58573$ |
$[0, 0, 0, -1836, 30672]$ |
\(y^2=x^3-1836x+30672\) |
3.4.0.a.1, 9.36.0.d.2, 12.8.0-3.a.1.3, 24.16.0-24.d.1.5, 36.72.0-9.d.2.4, $\ldots$ |
$[]$ |
| 1728.z2 |
1728s2 |
1728.z |
1728s |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{27} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.4 |
3B |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$1152$ |
$0.724516$ |
$-1167051/512$ |
$1.04966$ |
$4.36018$ |
$[0, 0, 0, -876, -13232]$ |
\(y^2=x^3-876x-13232\) |
3.4.0.a.1, 9.36.0.d.1, 12.8.0-3.a.1.4, 24.16.0-24.d.1.6, 36.72.0-9.d.1.4, $\ldots$ |
$[]$ |
| 1728.z3 |
1728s1 |
1728.z |
1728s |
$3$ |
$9$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{21} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.1 |
3Cs |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.175210$ |
$9261/8$ |
$1.19875$ |
$3.34098$ |
$[0, 0, 0, 84, 208]$ |
\(y^2=x^3+84x+208\) |
3.12.0.a.1, 9.36.0.a.1, 12.24.0-3.a.1.2, 24.48.1-24.ci.1.2, 36.72.0-9.a.1.4, $\ldots$ |
$[]$ |
| 1728.ba1 |
1728k1 |
1728.ba |
1728k |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$-0.021022$ |
$-3072$ |
$0.94639$ |
$3.17564$ |
$[0, 0, 0, -48, 160]$ |
\(y^2=x^3-48x+160\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[]$ |
| 1728.bb1 |
1728t1 |
1728.bb |
1728t |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$-0.021022$ |
$-3072$ |
$0.94639$ |
$3.17564$ |
$[0, 0, 0, -48, -160]$ |
\(y^2=x^3-48x-160\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[]$ |
