| 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 |
| 5292.a1 |
5292f2 |
5292.a |
5292f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{11} \cdot 7^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$42$ |
$16$ |
$0$ |
$3.306544910$ |
$1$ |
|
$2$ |
$31104$ |
$1.745150$ |
$32710656/343$ |
$0.99148$ |
$5.43607$ |
$[0, 0, 0, -116424, 15150996]$ |
\(y^2=x^3-116424x+15150996\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 21.8.0-3.a.1.2, 42.16.0-42.b.1.2 |
$[(133, 1421)]$ |
| 5292.a2 |
5292f1 |
5292.a |
5292f |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$42$ |
$16$ |
$0$ |
$1.102181636$ |
$1$ |
|
$4$ |
$10368$ |
$1.195843$ |
$221184/7$ |
$0.96329$ |
$4.59705$ |
$[0, 0, 0, -10584, -407484]$ |
\(y^2=x^3-10584x-407484\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 21.8.0-3.a.1.1, 42.16.0-42.b.1.1 |
$[(-56, 98)]$ |
| 5292.b1 |
5292g2 |
5292.b |
5292g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{5} \cdot 7^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$84$ |
$16$ |
$0$ |
$0.325018566$ |
$1$ |
|
$8$ |
$10368$ |
$1.110451$ |
$-2431344/343$ |
$0.85839$ |
$4.38955$ |
$[0, 0, 0, -5439, -172186]$ |
\(y^2=x^3-5439x-172186\) |
3.4.0.a.1, 12.8.0-3.a.1.4, 21.8.0-3.a.1.1, 84.16.0.? |
$[(175, 2058)]$ |
| 5292.b2 |
5292g1 |
5292.b |
5292g |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$84$ |
$16$ |
$0$ |
$0.975055700$ |
$1$ |
|
$2$ |
$3456$ |
$0.561145$ |
$11664/7$ |
$0.89152$ |
$3.48506$ |
$[0, 0, 0, 441, 686]$ |
\(y^2=x^3+441x+686\) |
3.4.0.a.1, 12.8.0-3.a.1.3, 21.8.0-3.a.1.2, 84.16.0.? |
$[(14, 98)]$ |
| 5292.c1 |
5292l1 |
5292.c |
5292l |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{11} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10368$ |
$1.374762$ |
$196608/7$ |
$0.96651$ |
$4.83958$ |
$[0, 0, 0, -21168, -1148364]$ |
\(y^2=x^3-21168x-1148364\) |
42.2.0.a.1 |
$[]$ |
| 5292.d1 |
5292i2 |
5292.d |
5292i |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1.096892372$ |
$1$ |
|
$2$ |
$6804$ |
$1.031164$ |
$0$ |
|
$4.16169$ |
$[0, 0, 0, 0, -64827]$ |
\(y^2=x^3-64827\) |
|
$[(147, 1764)]$ |
| 5292.d2 |
5292i1 |
5292.d |
5292i |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$3.290677116$ |
$1$ |
|
$4$ |
$2268$ |
$0.481858$ |
$0$ |
|
$3.39288$ |
$[0, 0, 0, 0, 2401]$ |
\(y^2=x^3+2401\) |
|
$[(15, 76)]$ |
| 5292.e1 |
5292j1 |
5292.e |
5292j |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$3780$ |
$0.806176$ |
$0$ |
|
$3.84680$ |
$[0, 0, 0, 0, -16807]$ |
\(y^2=x^3-16807\) |
|
$[]$ |
| 5292.e2 |
5292j2 |
5292.e |
5292j |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$11340$ |
$1.355482$ |
$0$ |
|
$4.61560$ |
$[0, 0, 0, 0, 453789]$ |
\(y^2=x^3+453789\) |
|
$[]$ |
| 5292.f1 |
5292b1 |
5292.f |
5292b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.373773159$ |
$1$ |
|
$2$ |
$4536$ |
$1.037226$ |
$0$ |
|
$4.17017$ |
$[0, 0, 0, 0, -67228]$ |
\(y^2=x^3-67228\) |
|
$[(44, 134)]$ |
| 5292.f2 |
5292b2 |
5292.f |
5292b |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$10.12131947$ |
$1$ |
|
$0$ |
$13608$ |
$1.586533$ |
$0$ |
|
$4.93897$ |
$[0, 0, 0, 0, 1815156]$ |
\(y^2=x^3+1815156\) |
|
$[(-11483/11, 1304423/11)]$ |
| 5292.g1 |
5292h2 |
5292.g |
5292h |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$0.750639728$ |
$1$ |
|
$2$ |
$1944$ |
$0.613577$ |
$0$ |
|
$3.57724$ |
$[0, 0, 0, 0, -5292]$ |
\(y^2=x^3-5292\) |
|
$[(21, 63)]$ |
| 5292.g2 |
5292h1 |
5292.g |
5292h |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{4} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$2.251919186$ |
$1$ |
|
$6$ |
$648$ |
$0.064270$ |
$0$ |
|
$2.80843$ |
$[0, 0, 0, 0, 196]$ |
\(y^2=x^3+196\) |
|
$[(-3, 13)]$ |
| 5292.h1 |
5292a2 |
5292.h |
5292a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$1620$ |
$0.382527$ |
$0$ |
|
$3.25386$ |
$[0, 0, 0, 0, -1323]$ |
\(y^2=x^3-1323\) |
|
$[]$ |
| 5292.h2 |
5292a1 |
5292.h |
5292a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$540$ |
$-0.166779$ |
$0$ |
|
$2.48506$ |
$[0, 0, 0, 0, 49]$ |
\(y^2=x^3+49\) |
|
$[]$ |
| 5292.i1 |
5292c1 |
5292.i |
5292c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.760093938$ |
$1$ |
|
$4$ |
$324$ |
$-0.491097$ |
$0$ |
|
$2.03115$ |
$[0, 0, 0, 0, -7]$ |
\(y^2=x^3-7\) |
|
$[(2, 1)]$ |
| 5292.i2 |
5292c2 |
5292.i |
5292c |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$2.280281814$ |
$1$ |
|
$2$ |
$972$ |
$0.058209$ |
$0$ |
|
$2.79995$ |
$[0, 0, 0, 0, 189]$ |
\(y^2=x^3+189\) |
|
$[(-5, 8)]$ |
| 5292.j1 |
5292k1 |
5292.j |
5292k |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1404$ |
$0.388589$ |
$0$ |
|
$3.26235$ |
$[0, 0, 0, 0, -1372]$ |
\(y^2=x^3-1372\) |
|
$[]$ |
| 5292.j2 |
5292k2 |
5292.j |
5292k |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$4212$ |
$0.937895$ |
$0$ |
|
$4.03115$ |
$[0, 0, 0, 0, 37044]$ |
\(y^2=x^3+37044\) |
|
$[]$ |
| 5292.k1 |
5292d1 |
5292.k |
5292d |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{5} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.101804680$ |
$1$ |
|
$10$ |
$3456$ |
$0.825456$ |
$196608/7$ |
$0.96651$ |
$4.07078$ |
$[0, 0, 0, -2352, 42532]$ |
\(y^2=x^3-2352x+42532\) |
42.2.0.a.1 |
$[(-28, 294)]$ |
| 5292.l1 |
5292e2 |
5292.l |
5292e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{11} \cdot 7^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$84$ |
$16$ |
$0$ |
$2.442568350$ |
$1$ |
|
$2$ |
$31104$ |
$1.659758$ |
$-2431344/343$ |
$0.85839$ |
$5.15835$ |
$[0, 0, 0, -48951, 4649022]$ |
\(y^2=x^3-48951x+4649022\) |
3.4.0.a.1, 12.8.0-3.a.1.3, 21.8.0-3.a.1.2, 84.16.0.? |
$[(-182, 2744)]$ |
| 5292.l2 |
5292e1 |
5292.l |
5292e |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{9} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$84$ |
$16$ |
$0$ |
$0.814189450$ |
$1$ |
|
$4$ |
$10368$ |
$1.110451$ |
$11664/7$ |
$0.89152$ |
$4.25386$ |
$[0, 0, 0, 3969, -18522]$ |
\(y^2=x^3+3969x-18522\) |
3.4.0.a.1, 12.8.0-3.a.1.4, 21.8.0-3.a.1.1, 84.16.0.? |
$[(7, 98)]$ |
| 5292.m1 |
5292m2 |
5292.m |
5292m |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{5} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$42$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10368$ |
$1.195843$ |
$32710656/343$ |
$0.99148$ |
$4.66727$ |
$[0, 0, 0, -12936, -561148]$ |
\(y^2=x^3-12936x-561148\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 21.8.0-3.a.1.1, 42.16.0-42.b.1.1 |
$[]$ |
| 5292.m2 |
5292m1 |
5292.m |
5292m |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$42$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3456$ |
$0.646537$ |
$221184/7$ |
$0.96329$ |
$3.82825$ |
$[0, 0, 0, -1176, 15092]$ |
\(y^2=x^3-1176x+15092\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 21.8.0-3.a.1.2, 42.16.0-42.b.1.2 |
$[]$ |
