| 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 |
| 248004.a1 |
248004a1 |
248004.a |
248004a |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 83^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$332$ |
$8$ |
$0$ |
$2.171286338$ |
$1$ |
|
$2$ |
$241920$ |
$0.714952$ |
$-131072$ |
$0.97669$ |
$2.77086$ |
$[0, 0, 0, -1992, 34445]$ |
\(y^2=x^3-1992x+34445\) |
4.4.0.a.1, 166.2.0.?, 332.8.0.? |
$[(83, 664)]$ |
| 248004.b1 |
248004b1 |
248004.b |
248004b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 83^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$996$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$7934976$ |
$2.550987$ |
$-810448/2241$ |
$0.78107$ |
$4.34816$ |
$[0, 0, 0, -764679, 618673534]$ |
\(y^2=x^3-764679x+618673534\) |
3.4.0.a.1, 12.8.0-3.a.1.3, 249.8.0.?, 996.16.0.? |
$[ ]$ |
| 248004.b2 |
248004b2 |
248004.b |
248004b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{7} \cdot 83^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$996$ |
$16$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$23804928$ |
$3.100292$ |
$539172272/1715361$ |
$0.88932$ |
$4.85130$ |
$[0, 0, 0, 6675441, -14078539514]$ |
\(y^2=x^3+6675441x-14078539514\) |
3.4.0.a.1, 12.8.0-3.a.1.4, 249.8.0.?, 996.16.0.? |
$[ ]$ |
| 248004.c1 |
248004c1 |
248004.c |
248004c |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{6} \cdot 83^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.2.0.1 |
|
$1992$ |
$4$ |
$0$ |
$1.731528522$ |
$1$ |
|
$10$ |
$84672$ |
$0.436049$ |
$1328$ |
$0.59874$ |
$2.26757$ |
$[0, 0, 0, 249, 830]$ |
\(y^2=x^3+249x+830\) |
4.2.0.a.1, 1992.4.0.? |
$[(7, 54), (-2, 18)]$ |
| 248004.d1 |
248004d1 |
248004.d |
248004d |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{19} \cdot 83^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$996$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$34384896$ |
$3.458790$ |
$1893932336/132328809$ |
$0.97047$ |
$5.21665$ |
$[0, 0, 0, 10147497, -136143628274]$ |
\(y^2=x^3+10147497x-136143628274\) |
996.2.0.? |
$[ ]$ |
| 248004.e1 |
248004e4 |
248004.e |
248004e |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 83^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$2.218505006$ |
$1$ |
|
$3$ |
$3471552$ |
$2.289886$ |
$54000$ |
$1.02720$ |
$4.25422$ |
$[0, 0, 0, -930015, 339641478]$ |
\(y^2=x^3-930015x+339641478\) |
|
$[(166, 13778)]$ |
| 248004.e2 |
248004e2 |
248004.e |
248004e |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 83^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-12$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$6.655515019$ |
$1$ |
|
$1$ |
$1157184$ |
$1.740578$ |
$54000$ |
$1.02720$ |
$3.72354$ |
$[0, 0, 0, -103335, -12579314]$ |
\(y^2=x^3-103335x-12579314\) |
|
$[(-81506/21, 4202290/21)]$ |
| 248004.e3 |
248004e1 |
248004.e |
248004e |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 83^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$13.31103003$ |
$1$ |
|
$1$ |
$578592$ |
$1.394005$ |
$0$ |
|
$3.22321$ |
$[0, 0, 0, 0, -571787]$ |
\(y^2=x^3-571787\) |
|
$[(838043/61, 747738180/61)]$ |
| 248004.e4 |
248004e3 |
248004.e |
248004e |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 83^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.83 |
2B |
|
|
|
$4.437010012$ |
$1$ |
|
$3$ |
$1735776$ |
$1.943312$ |
$0$ |
|
$3.75389$ |
$[0, 0, 0, 0, 15438249]$ |
\(y^2=x^3+15438249\) |
|
$[(183, 4644)]$ |
| 248004.f1 |
248004f2 |
248004.f |
248004f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 83^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$70.78904309$ |
$1$ |
|
$0$ |
$18573408$ |
$2.910835$ |
$0$ |
|
$4.68861$ |
$[0, 0, 0, 0, -5125498668]$ |
\(y^2=x^3-5125498668\) |
|
$[(16701073636171432306885047026157/97846995026599, 12662719290284918701835317878392896237047895395/97846995026599)]$ |
| 248004.f2 |
248004f1 |
248004.f |
248004f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 83^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$23.59634769$ |
$1$ |
|
$2$ |
$6191136$ |
$2.361526$ |
$0$ |
|
$4.15793$ |
$[0, 0, 0, 0, 189833284]$ |
\(y^2=x^3+189833284\) |
|
$[(58147077716/6731, 14637429798987270/6731)]$ |
| 248004.g1 |
248004g1 |
248004.g |
248004g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 83^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$6.128407707$ |
$1$ |
|
$0$ |
$74592$ |
$0.152107$ |
$0$ |
|
$2.02343$ |
$[0, 0, 0, 0, -332]$ |
\(y^2=x^3-332\) |
|
$[(557/7, 11565/7)]$ |
| 248004.g2 |
248004g2 |
248004.g |
248004g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 83^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$2.042802569$ |
$1$ |
|
$2$ |
$223776$ |
$0.701413$ |
$0$ |
|
$2.55411$ |
$[0, 0, 0, 0, 8964]$ |
\(y^2=x^3+8964\) |
|
$[(21, 135)]$ |
| 248004.h1 |
248004h1 |
248004.h |
248004h |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{8} \cdot 3^{6} \cdot 83^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.2.0.1 |
|
$24$ |
$4$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$7027776$ |
$2.645470$ |
$1328$ |
$0.59874$ |
$4.40207$ |
$[0, 0, 0, 1715361, -474583210]$ |
\(y^2=x^3+1715361x-474583210\) |
4.2.0.a.1, 24.4.0-4.a.1.1 |
$[ ]$ |
| 248004.i1 |
248004i1 |
248004.i |
248004i |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 83^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$332$ |
$8$ |
$0$ |
$41.02425217$ |
$1$ |
|
$0$ |
$20079360$ |
$2.924370$ |
$-131072$ |
$0.97669$ |
$4.90536$ |
$[0, 0, 0, -13722888, -19695203215]$ |
\(y^2=x^3-13722888x-19695203215\) |
4.4.0.a.1, 166.2.0.?, 332.8.0.? |
$[(535751977269700493930/342417583, 4577968465589037431870504584045/342417583)]$ |
| 248004.j1 |
248004j2 |
248004.j |
248004j |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 83^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$996$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$29756160$ |
$2.939667$ |
$680136784/186003$ |
$0.85565$ |
$4.74895$ |
$[0, 0, 0, -7212783, -5414822890]$ |
\(y^2=x^3-7212783x-5414822890\) |
2.3.0.a.1, 12.6.0.a.1, 332.6.0.?, 996.12.0.? |
$[ ]$ |
| 248004.j2 |
248004j1 |
248004.j |
248004j |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 83^{2} \) |
\( - 2^{4} \cdot 3^{12} \cdot 83^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$996$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$14878080$ |
$2.593094$ |
$44957696/60507$ |
$0.95194$ |
$4.32973$ |
$[0, 0, 0, 1157352, -551774455]$ |
\(y^2=x^3+1157352x-551774455\) |
2.3.0.a.1, 12.6.0.b.1, 166.6.0.?, 996.12.0.? |
$[ ]$ |
