| 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 |
| 4290.bb8 |
4290bb5 |
4290.bb |
4290bb |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.8, 3.8.0.1 |
2B, 3B.1.1 |
$17160$ |
$384$ |
$5$ |
$2.145205242$ |
$1$ |
|
$12$ |
$55296$ |
$1.929352$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.48106$ |
$[1, 0, 0, 80420, 10438352]$ |
\(y^2+xy=x^3+80420x+10438352\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.c.1.2, 6.24.0-6.a.1.4, 12.96.0-12.c.3.7, $\ldots$ |
$[(-82, 1856)]$ |
| 12870.c8 |
12870p5 |
12870.c |
12870p |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$442368$ |
$2.478657$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.54131$ |
$[1, -1, 0, 723780, -281835504]$ |
\(y^2+xy=x^3-x^2+723780x-281835504\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 12.96.0-12.c.3.3, $\ldots$ |
$[]$ |
| 21450.r8 |
21450d4 |
21450.r |
21450d |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{18} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$8.949379149$ |
$1$ |
|
$0$ |
$1327104$ |
$2.734070$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.56481$ |
$[1, 1, 0, 2010500, 1304794000]$ |
\(y^2+xy=x^3+x^2+2010500x+1304794000\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(-23841/7, 5074028/7)]$ |
| 34320.bb8 |
34320bn4 |
34320.bb |
34320bn |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{18} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.7, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$5.762060812$ |
$1$ |
|
$5$ |
$1327104$ |
$2.622501$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.18616$ |
$[0, -1, 0, 1286720, -668054528]$ |
\(y^2=x^3-x^2+1286720x-668054528\) |
2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.c.1.1, 6.12.0.a.1, 12.96.0-12.c.3.8, $\ldots$ |
$[(6378, 516670)]$ |
| 47190.bl8 |
47190bh4 |
47190.bl |
47190bh |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 11^{10} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$6635520$ |
$3.128300$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.59669$ |
$[1, 0, 1, 9730817, -13883715694]$ |
\(y^2+xy+y=x^3+9730817x-13883715694\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
| 55770.bc8 |
55770bc4 |
55770.bc |
55770bc |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$2.011113849$ |
$1$ |
|
$2$ |
$9289728$ |
$3.211826$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.60285$ |
$[1, 0, 1, 13590976, 22919468366]$ |
\(y^2+xy+y=x^3+13590976x+22919468366\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.24.0-6.a.1.3, 12.96.0-12.c.3.6, $\ldots$ |
$[(2081, 244347)]$ |
| 64350.fe8 |
64350el4 |
64350.fe |
64350el |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{18} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$10616832$ |
$3.283379$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.60799$ |
$[1, -1, 1, 18094495, -35211343503]$ |
\(y^2+xy+y=x^3-x^2+18094495x-35211343503\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
| 102960.ci8 |
102960dj4 |
102960.ci |
102960dj |
$8$ |
$12$ |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{18} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$4$ |
$2$ |
$1$ |
$10616832$ |
$3.171806$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.26363$ |
$[0, 0, 0, 11580477, 18025891778]$ |
\(y^2=x^3+11580477x+18025891778\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.96.0-12.c.3.4, $\ldots$ |
$[]$ |
| 137280.e8 |
137280gn5 |
137280.e |
137280gn |
$8$ |
$12$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{24} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.7, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$10616832$ |
$2.969074$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$4.92997$ |
$[0, -1, 0, 5146879, 5339289345]$ |
\(y^2=x^3-x^2+5146879x+5339289345\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$ |
$[]$ |
| 137280.fi8 |
137280bs4 |
137280.fi |
137280bs |
$8$ |
$12$ |
\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{24} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.8, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$11.81656552$ |
$1$ |
|
$1$ |
$10616832$ |
$2.969074$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$4.92997$ |
$[0, 1, 0, 5146879, -5339289345]$ |
\(y^2=x^3+x^2+5146879x-5339289345\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$ |
$[(4870021/31, 11573045484/31)]$ |
| 141570.dp8 |
141570ca5 |
141570.dp |
141570ca |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 11^{10} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$4$ |
$2$ |
$0$ |
$53084160$ |
$3.677605$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.63405$ |
$[1, -1, 1, 87577357, 374860323731]$ |
\(y^2+xy+y=x^3-x^2+87577357x+374860323731\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
| 167310.fr8 |
167310w4 |
167310.fr |
167310w |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.8, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$74317824$ |
$3.761135$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.63913$ |
$[1, -1, 1, 122318788, -618825645889]$ |
\(y^2+xy+y=x^3-x^2+122318788x-618825645889\) |
2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.c.1.2, 6.24.0-6.a.1.1, 12.96.0-12.c.3.2, $\ldots$ |
$[]$ |
| 171600.el8 |
171600bg4 |
171600.el |
171600bg |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \) |
\( - 2^{18} \cdot 3^{3} \cdot 5^{18} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$31850496$ |
$3.427219$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.29484$ |
$[0, 1, 0, 32167992, -83442480012]$ |
\(y^2=x^3+x^2+32167992x-83442480012\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
| 210210.cs8 |
210210da4 |
210210.cs |
210210da |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 7^{6} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$120120$ |
$384$ |
$5$ |
$2.928720341$ |
$4$ |
$2$ |
$4$ |
$15925248$ |
$2.902309$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$4.69321$ |
$[1, 1, 1, 3940579, -3576414157]$ |
\(y^2+xy+y=x^3+x^2+3940579x-3576414157\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(2267, 129304)]$ |
| 235950.eq8 |
235950eq4 |
235950.eq |
235950eq |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{18} \cdot 11^{10} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.6, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$4$ |
$2$ |
$0$ |
$159252480$ |
$3.933018$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.64916$ |
$[1, 1, 1, 243270437, -1735464461719]$ |
\(y^2+xy+y=x^3+x^2+243270437x-1735464461719\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.5, $\ldots$ |
$[]$ |
| 278850.ey8 |
278850ey5 |
278850.ey |
278850ey |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{18} \cdot 11^{4} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$7.014498953$ |
$1$ |
|
$2$ |
$222953472$ |
$4.016548$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.65383$ |
$[1, 1, 1, 339774412, 2864933545781]$ |
\(y^2+xy+y=x^3+x^2+339774412x+2864933545781\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(4919, 2155163)]$ |
| 377520.bu8 |
377520bu5 |
377520.bu |
377520bu |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \) |
\( - 2^{18} \cdot 3^{3} \cdot 5^{12} \cdot 11^{10} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$159252480$ |
$3.821445$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.33813$ |
$[0, -1, 0, 155693080, 888557804400]$ |
\(y^2=x^3-x^2+155693080x+888557804400\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[]$ |
| 411840.hc8 |
411840hc4 |
411840.hc |
411840hc |
$8$ |
$12$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{24} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$2.131564569$ |
$1$ |
|
$5$ |
$84934656$ |
$3.518379$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.02090$ |
$[0, 0, 0, 46321908, -144207134224]$ |
\(y^2=x^3+46321908x-144207134224\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(3902, 309760)]$ |
| 411840.nt8 |
411840nt5 |
411840.nt |
411840nt |
$8$ |
$12$ |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \) |
\( - 2^{24} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$2.663552039$ |
$1$ |
|
$3$ |
$84934656$ |
$3.518379$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.02090$ |
$[0, 0, 0, 46321908, 144207134224]$ |
\(y^2=x^3+46321908x+144207134224\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.3, $\ldots$ |
$[(24258, 3942400)]$ |
| 446160.a8 |
446160a4 |
446160.a |
446160a |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \) |
\( - 2^{18} \cdot 3^{3} \cdot 5^{12} \cdot 11^{4} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.6.0.1, 3.4.0.1 |
2B, 3B |
$17160$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$222953472$ |
$3.904976$ |
$57519563401957999679/80296734375000000$ |
$0.99843$ |
$5.34663$ |
$[0, -1, 0, 217455624, -1466845975440]$ |
\(y^2=x^3-x^2+217455624x-1466845975440\) |
2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.96.0-12.c.3.5, $\ldots$ |
$[]$ |
