| 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 |
| 1764.a1 |
1764e2 |
1764.a |
1764e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.24.0.2 |
2Cn, 3B.1.1 |
$252$ |
$864$ |
$28$ |
$2.704530736$ |
$1$ |
|
$6$ |
$3780$ |
$1.317226$ |
$406749952$ |
$0.99897$ |
$5.98705$ |
$[0, 0, 0, -62769, 6052921]$ |
\(y^2=x^3-62769x+6052921\) |
2.2.0.a.1, 3.8.0-3.a.1.2, 6.16.0-6.a.1.2, 9.24.0-9.b.1.2, 12.32.0-12.a.1.4, $\ldots$ |
$[(144, 13)]$ |
| 1764.a2 |
1764e1 |
1764.a |
1764e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.24.0.4 |
2Cn, 3B.1.2 |
$252$ |
$864$ |
$28$ |
$0.901510245$ |
$1$ |
|
$2$ |
$1260$ |
$0.767920$ |
$1792$ |
$0.89152$ |
$4.33728$ |
$[0, 0, 0, -1029, 2401]$ |
\(y^2=x^3-1029x+2401\) |
2.2.0.a.1, 3.8.0-3.a.1.1, 6.16.0-6.a.1.1, 9.24.0-9.b.1.1, 12.32.0-12.a.2.1, $\ldots$ |
$[(0, 49)]$ |
| 1764.b1 |
1764i2 |
1764.b |
1764i |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$5376$ |
$1.396481$ |
$109744/9$ |
$0.87899$ |
$5.51894$ |
$[0, 0, 0, -19551, 974806]$ |
\(y^2=x^3-19551x+974806\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.a.1, 84.12.0.? |
$[]$ |
| 1764.b2 |
1764i1 |
1764.b |
1764i |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$2688$ |
$1.049908$ |
$16384/3$ |
$1.03704$ |
$4.89363$ |
$[0, 0, 0, -4116, -84035]$ |
\(y^2=x^3-4116x-84035\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.b.1, 42.6.0.a.1, 84.12.0.? |
$[]$ |
| 1764.c1 |
1764h1 |
1764.c |
1764h |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{11} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10080$ |
$1.779987$ |
$401408/243$ |
$1.33755$ |
$5.95273$ |
$[0, 0, 0, 57624, -1142876]$ |
\(y^2=x^3+57624x-1142876\) |
6.2.0.a.1 |
$[]$ |
| 1764.d1 |
1764c1 |
1764.d |
1764c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.345779633$ |
$1$ |
|
$6$ |
$144$ |
$-0.260048$ |
$0$ |
|
$2.70055$ |
$[0, 0, 0, 0, -28]$ |
\(y^2=x^3-28\) |
|
$[(4, 6)]$ |
| 1764.d2 |
1764c2 |
1764.d |
1764c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.037338899$ |
$1$ |
|
$2$ |
$432$ |
$0.289258$ |
$0$ |
|
$3.58234$ |
$[0, 0, 0, 0, 756]$ |
\(y^2=x^3+756\) |
|
$[(-3, 27)]$ |
| 1764.e1 |
1764b4 |
1764.e |
1764b |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.161372234$ |
$1$ |
|
$3$ |
$1728$ |
$1.053419$ |
$54000$ |
$1.02720$ |
$5.08404$ |
$[0, 0, 0, -6615, 203742]$ |
\(y^2=x^3-6615x+203742\) |
|
$[(-66, 594)]$ |
| 1764.e2 |
1764b2 |
1764.e |
1764b |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.053790744$ |
$1$ |
|
$7$ |
$576$ |
$0.504113$ |
$54000$ |
$1.02720$ |
$4.20225$ |
$[0, 0, 0, -735, -7546]$ |
\(y^2=x^3-735x-7546\) |
|
$[(-17, 6)]$ |
| 1764.e3 |
1764b1 |
1764.e |
1764b |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$0.526895372$ |
$1$ |
|
$9$ |
$288$ |
$0.157540$ |
$0$ |
|
$3.37090$ |
$[0, 0, 0, 0, -343]$ |
\(y^2=x^3-343\) |
|
$[(14, 49)]$ |
| 1764.e4 |
1764b3 |
1764.e |
1764b |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$1.580686117$ |
$1$ |
|
$3$ |
$864$ |
$0.706846$ |
$0$ |
|
$4.25269$ |
$[0, 0, 0, 0, 9261]$ |
\(y^2=x^3+9261\) |
|
$[(7, 98)]$ |
| 1764.f1 |
1764a2 |
1764.f |
1764a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$3024$ |
$1.262213$ |
$0$ |
|
$5.14421$ |
$[0, 0, 0, 0, -259308]$ |
\(y^2=x^3-259308\) |
|
$[]$ |
| 1764.f2 |
1764a1 |
1764.f |
1764a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$1008$ |
$0.712907$ |
$0$ |
|
$4.26242$ |
$[0, 0, 0, 0, 9604]$ |
\(y^2=x^3+9604\) |
|
$[]$ |
| 1764.g1 |
1764f4 |
1764.g |
1764f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$13824$ |
$1.937071$ |
$2640279346000/3087$ |
$1.02245$ |
$7.01162$ |
$[0, 0, 0, -806295, -278668978]$ |
\(y^2=x^3-806295x-278668978\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.5, 21.8.0-3.a.1.1, $\ldots$ |
$[]$ |
| 1764.g2 |
1764f3 |
1764.g |
1764f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{7} \cdot 7^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$6912$ |
$1.590496$ |
$-10061824000/352947$ |
$1.07286$ |
$5.90349$ |
$[0, 0, 0, -49980, -4429159]$ |
\(y^2=x^3-49980x-4429159\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.2, 21.8.0-3.a.1.1, $\ldots$ |
$[]$ |
| 1764.g3 |
1764f2 |
1764.g |
1764f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$4608$ |
$1.387764$ |
$9826000/5103$ |
$0.97243$ |
$5.33927$ |
$[0, 0, 0, -12495, -172186]$ |
\(y^2=x^3-12495x-172186\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.7, 21.8.0-3.a.1.2, $\ldots$ |
$[]$ |
| 1764.g4 |
1764f1 |
1764.g |
1764f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$2304$ |
$1.041191$ |
$2048000/1323$ |
$1.10843$ |
$4.75859$ |
$[0, 0, 0, 2940, -20923]$ |
\(y^2=x^3+2940x-20923\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.5, 21.8.0-3.a.1.2, $\ldots$ |
$[]$ |
| 1764.h1 |
1764d1 |
1764.h |
1764d |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{11} \cdot 7^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.401101671$ |
$1$ |
|
$6$ |
$1440$ |
$0.807032$ |
$401408/243$ |
$1.33755$ |
$4.39087$ |
$[0, 0, 0, 1176, 3332]$ |
\(y^2=x^3+1176x+3332\) |
6.2.0.a.1 |
$[(16, 162)]$ |
| 1764.i1 |
1764g2 |
1764.i |
1764g |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.423526$ |
$109744/9$ |
$0.87899$ |
$3.95708$ |
$[0, 0, 0, -399, -2842]$ |
\(y^2=x^3-399x-2842\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.a.1, 84.12.0.? |
$[]$ |
| 1764.i2 |
1764g1 |
1764.i |
1764g |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.076952$ |
$16384/3$ |
$1.03704$ |
$3.33176$ |
$[0, 0, 0, -84, 245]$ |
\(y^2=x^3-84x+245\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.b.1, 42.6.0.a.1, 84.12.0.? |
$[]$ |
| 1764.j1 |
1764j2 |
1764.j |
1764j |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$540$ |
$0.344271$ |
$406749952$ |
$0.99897$ |
$4.42519$ |
$[0, 0, 0, -1281, -17647]$ |
\(y^2=x^3-1281x-17647\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.1, $\ldots$ |
$[]$ |
| 1764.j2 |
1764j1 |
1764.j |
1764j |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$252$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$-0.205035$ |
$1792$ |
$0.89152$ |
$2.77542$ |
$[0, 0, 0, -21, -7]$ |
\(y^2=x^3-21x-7\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.2, $\ldots$ |
$[]$ |
| 1764.k1 |
1764k2 |
1764.k |
1764k |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4608$ |
$1.198275$ |
$20720464/63$ |
$0.91015$ |
$5.43908$ |
$[0, 0, 0, -16023, -778610]$ |
\(y^2=x^3-16023x-778610\) |
2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.? |
$[]$ |
| 1764.k2 |
1764k1 |
1764.k |
1764k |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{7} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$2304$ |
$0.851701$ |
$-16384/147$ |
$1.05520$ |
$4.48774$ |
$[0, 0, 0, -588, -22295]$ |
\(y^2=x^3-588x-22295\) |
2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.? |
$[]$ |
