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 |
27672.a2 |
27672d2 |
27672.a |
27672d |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 1153 \) |
\( - 2^{11} \cdot 3^{5} \cdot 1153^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$27672$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$6896640$ |
$3.664673$ |
$-7202235579917551873106245634/570929018495117877747$ |
$1.06156$ |
$7.01679$ |
$[0, -1, 0, -510925824, -4445268513876]$ |
\(y^2=x^3-x^2-510925824x-4445268513876\) |
2.3.0.a.1, 24.6.0.b.1, 4612.6.0.?, 27672.12.0.? |
$[]$ |
79530.v1 |
79530u6 |
79530.v |
79530u |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 241 \) |
\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 241^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$57840$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$12320768$ |
$3.255619$ |
$157232393831032011314187823434241/210834030$ |
$1.01467$ |
$6.57001$ |
$[1, 0, 0, -1124448160, -14513096227630]$ |
\(y^2+xy=x^3-1124448160x-14513096227630\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 120.48.0.?, $\ldots$ |
$[]$ |
90174.ba1 |
90174ba6 |
90174.ba |
90174ba |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 19 \cdot 113 \) |
\( 2 \cdot 3 \cdot 7 \cdot 19 \cdot 113^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$721392$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$3997696$ |
$2.556595$ |
$17750035721051160858939234817/10189662$ |
$0.99134$ |
$5.70106$ |
$[1, 0, 0, -54344864, -154205061150]$ |
\(y^2+xy=x^3-54344864x-154205061150\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 112.48.0.?, 912.48.0.?, $\ldots$ |
$[]$ |
92778.bb6 |
92778v5 |
92778.bb |
92778v |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 47^{2} \) |
\( - 2^{2} \cdot 3 \cdot 7^{16} \cdot 47^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.114 |
2B |
$2256$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$72351744$ |
$4.047409$ |
$1065104896666636223/880938523538983308$ |
$1.06468$ |
$6.28387$ |
$[1, 0, 0, 46998638, -4686753911728]$ |
\(y^2+xy=x^3+46998638x-4686753911728\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0-8.n.1.7, 12.12.0.g.1, $\ldots$ |
$[]$ |
98469.g1 |
98469e1 |
98469.g |
98469e |
$1$ |
$1$ |
\( 3^{3} \cdot 7 \cdot 521 \) |
\( - 3^{11} \cdot 7^{4} \cdot 521^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3126$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$18503424$ |
$3.180546$ |
$-12057468028065957881966592/339551247161$ |
$1.00271$ |
$6.07406$ |
$[0, 0, 1, -268300863, -1691535894559]$ |
\(y^2+y=x^3-268300863x-1691535894559\) |
3126.2.0.? |
$[]$ |
122070.r1 |
122070t8 |
122070.r |
122070t |
$8$ |
$16$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 313 \) |
\( 2 \cdot 3 \cdot 5^{8} \cdot 13 \cdot 313 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.14 |
2B |
$390624$ |
$768$ |
$13$ |
$1$ |
$256$ |
$2$ |
$0$ |
$116916224$ |
$4.143639$ |
$14551803469961881301880007324200000001/9536718750$ |
$1.03071$ |
$7.30603$ |
$[1, 0, 0, -50862500000, -4415146156596318]$ |
\(y^2+xy=x^3-50862500000x-4415146156596318\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 32.96.0-32.e.2.4, $\ldots$ |
$[]$ |
166566.bi1 |
166566i4 |
166566.bi |
166566i |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 17 \cdot 23 \cdot 71 \) |
\( 2 \cdot 3 \cdot 17 \cdot 23 \cdot 71 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$666264$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$753664$ |
$1.620253$ |
$77531644541319905014273/166566$ |
$0.98737$ |
$4.38363$ |
$[1, 0, 0, -888352, -322348390]$ |
\(y^2+xy=x^3-888352x-322348390\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 408.24.0.?, 6532.12.0.?, $\ldots$ |
$[]$ |
172042.g1 |
172042o1 |
172042.g |
172042o |
$1$ |
$1$ |
\( 2 \cdot 13^{2} \cdot 509 \) |
\( - 2^{53} \cdot 13^{9} \cdot 509 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$52936$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$265898880$ |
$4.403893$ |
$-2977809191050971718605709/4584664420663164928$ |
$1.00154$ |
$6.58956$ |
$[1, 1, 0, -6584979716, -205950335198512]$ |
\(y^2+xy=x^3+x^2-6584979716x-205950335198512\) |
52936.2.0.? |
$[]$ |
183872.ck1 |
183872bj2 |
183872.ck |
183872bj |
$2$ |
$2$ |
\( 2^{6} \cdot 13^{2} \cdot 17 \) |
\( 2^{29} \cdot 13^{8} \cdot 17^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$681246720$ |
$4.667618$ |
$729596217166155478587889/697759680872204288$ |
$1.03716$ |
$6.83164$ |
$[0, -1, 0, -20285527201, -1111132282168767]$ |
\(y^2=x^3-x^2-20285527201x-1111132282168767\) |
2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.? |
$[]$ |
184002.y1 |
184002e6 |
184002.y |
184002e |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 337 \) |
\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \cdot 337^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$113232$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$66322432$ |
$3.567085$ |
$8788348818995733772093682020118017/806112762$ |
$1.01170$ |
$6.44730$ |
$[1, 0, 0, -4299268064, -108502897189050]$ |
\(y^2+xy=x^3-4299268064x-108502897189050\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 168.48.0.?, $\ldots$ |
$[]$ |
188538.e2 |
188538x1 |
188538.e |
188538x |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 67^{2} \) |
\( - 2^{28} \cdot 3^{5} \cdot 7 \cdot 67^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$5628$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$387806720$ |
$4.174049$ |
$-17665993561158307/456608710656$ |
$1.10751$ |
$6.19873$ |
$[1, 1, 0, -1631908708, -25935309711920]$ |
\(y^2+xy=x^3+x^2-1631908708x-25935309711920\) |
2.3.0.a.1, 84.6.0.?, 268.6.0.?, 2814.6.0.?, 5628.12.0.? |
$[]$ |
192027.q1 |
192027n6 |
192027.q |
192027n |
$6$ |
$8$ |
\( 3 \cdot 11^{2} \cdot 23^{2} \) |
\( 3 \cdot 11^{7} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$64880640$ |
$3.881802$ |
$89254274298475942657/17457$ |
$1.00726$ |
$6.50520$ |
$[1, 0, 1, -5959495270, -177077568797197]$ |
\(y^2+xy+y=x^3-5959495270x-177077568797197\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 48.48.0-48.f.1.24, 66.6.0.a.1, $\ldots$ |
$[]$ |
194025.bf1 |
194025bf1 |
194025.bf |
194025bf |
$1$ |
$1$ |
\( 3 \cdot 5^{2} \cdot 13 \cdot 199 \) |
\( - 3^{8} \cdot 5^{8} \cdot 13^{3} \cdot 199^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$5174$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$127872000$ |
$3.902668$ |
$-50623694557243921369914880000/113595028255683$ |
$1.07912$ |
$6.48582$ |
$[0, -1, 1, -5633738958, -162756440227807]$ |
\(y^2+y=x^3-x^2-5633738958x-162756440227807\) |
5174.2.0.? |
$[]$ |
197610.w1 |
197610b4 |
197610.w |
197610b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 941 \) |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 941 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$112920$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$4358144$ |
$2.099957$ |
$44405909975117603989762561/1383270$ |
$1.03912$ |
$4.84297$ |
$[1, 0, 0, -7377440, -7713318438]$ |
\(y^2+xy=x^3-7377440x-7713318438\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.bb.1.14, 18820.12.0.?, $\ldots$ |
$[]$ |
209706.i2 |
209706j2 |
209706.i |
209706j |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 7 \cdot 4993 \) |
\( - 2^{2} \cdot 3^{11} \cdot 7^{4} \cdot 4993^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$59916$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1505501184$ |
$4.716606$ |
$30098262739826310413799910900470911/26360603551751862471828764258412$ |
$1.02210$ |
$6.47897$ |
$[1, 1, 1, 6480461064, 143879475442341]$ |
\(y^2+xy+y=x^3+x^2+6480461064x+143879475442341\) |
2.3.0.a.1, 6.6.0.a.1, 19972.6.0.?, 59916.12.0.? |
$[]$ |
218886.d1 |
218886c4 |
218886.d |
218886c |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 191^{2} \) |
\( 2^{2} \cdot 3 \cdot 191^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$4584$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$37355520$ |
$3.293205$ |
$202006784792779777/2292$ |
$0.98999$ |
$5.80343$ |
$[1, 0, 0, -445944504, -3624714373812]$ |
\(y^2+xy=x^3-445944504x-3624714373812\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.1, 1146.6.0.?, 1528.24.0.?, $\ldots$ |
$[]$ |
219558.f1 |
219558q1 |
219558.f |
219558q |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 23 \cdot 37 \cdot 43 \) |
\( - 2^{20} \cdot 3^{20} \cdot 23 \cdot 37 \cdot 43 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$146372$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$963532800$ |
$4.835457$ |
$-8809268125336410789565083264617658411625/133789805797224480768$ |
$1.03407$ |
$7.47816$ |
$[1, 1, 0, -430267660870, -108631778202449132]$ |
\(y^2+xy=x^3+x^2-430267660870x-108631778202449132\) |
146372.2.0.? |
$[]$ |
228144.cv1 |
228144v6 |
228144.cv |
228144v |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 97 \) |
\( 2^{14} \cdot 3 \cdot 7^{8} \cdot 97^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.13 |
2B |
$32592$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$1$ |
$150994944$ |
$4.082657$ |
$2841072266191027343455282177/5532492$ |
$1.03645$ |
$6.74412$ |
$[0, 1, 0, -23133193232, -1354265967127788]$ |
\(y^2=x^3+x^2-23133193232x-1354265967127788\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$ |
$[]$ |
236778.m2 |
236778m2 |
236778.m |
236778m |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 31 \cdot 67 \) |
\( - 2^{5} \cdot 3 \cdot 19^{2} \cdot 31 \cdot 67^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$947112$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$63436800$ |
$3.687695$ |
$-16878900309620470413760819550233/1958340275590921188072864$ |
$0.99459$ |
$5.81047$ |
$[1, 0, 1, -534408650, -4755606692644]$ |
\(y^2+xy+y=x^3-534408650x-4755606692644\) |
2.3.0.a.1, 744.6.0.?, 5092.6.0.?, 947112.12.0.? |
$[]$ |
255990.dv3 |
255990dv5 |
255990.dv |
255990dv |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \cdot 53 \) |
\( - 2 \cdot 3 \cdot 5^{4} \cdot 7^{24} \cdot 23 \cdot 53 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.55 |
2B |
$409584$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$169869312$ |
$3.877262$ |
$-2034405522757878898545944661601/875765703948414221830571250$ |
$0.99233$ |
$5.64880$ |
$[1, 0, 0, -263980150, -2180046906250]$ |
\(y^2+xy=x^3-263980150x-2180046906250\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 112.48.0.?, 184.48.0.?, $\ldots$ |
$[]$ |
300060.b1 |
300060b1 |
300060.b |
300060b |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 5 \cdot 1667 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{3} \cdot 1667 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$33340$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1501446240$ |
$5.101357$ |
$20289498132023711275180341010718329936/208375$ |
$1.03789$ |
$7.77371$ |
$[0, 0, 0, -3247170020823, -2252193271681168978]$ |
\(y^2=x^3-3247170020823x-2252193271681168978\) |
33340.2.0.? |
$[]$ |
311610.bd1 |
311610bd4 |
311610.bd |
311610bd |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 47 \) |
\( 2 \cdot 3^{3} \cdot 5^{5} \cdot 13 \cdot 17^{4} \cdot 47 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.6.0.1 |
2B |
$1246440$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$53084160$ |
$3.208900$ |
$18389710204702022109340521737569/8611537106250$ |
$0.99103$ |
$5.69108$ |
$[1, 1, 1, -549900006, -4963565397831]$ |
\(y^2+xy+y=x^3+x^2-549900006x-4963565397831\) |
2.3.0.a.1, 4.6.0.c.1, 136.12.0.?, 260.12.0.?, 1128.12.0.?, $\ldots$ |
$[]$ |
316680.ca3 |
316680ca5 |
316680.ca |
316680ca |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 29 \) |
\( - 2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{24} \cdot 13^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.55 |
2B |
$48720$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$1$ |
$415236096$ |
$4.402634$ |
$-5249562401418013365341039985602/70420471124711699773447575$ |
$1.00583$ |
$6.18865$ |
$[0, 1, 0, -4598079200, -121393199757600]$ |
\(y^2=x^3+x^2-4598079200x-121393199757600\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 40.48.0-40.ca.2.3, 112.48.0.?, $\ldots$ |
$[]$ |
333030.x1 |
333030x4 |
333030.x |
333030x |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 653 \) |
\( 2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 653 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1332120$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$5570560$ |
$1.933790$ |
$4957468492352708582138881/666060$ |
$0.94611$ |
$4.47177$ |
$[1, 0, 0, -3552320, -2577306828]$ |
\(y^2+xy=x^3-3552320x-2577306828\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 204.12.0.?, 408.24.0.?, $\ldots$ |
$[]$ |
349522.b1 |
349522b1 |
349522.b |
349522b |
$1$ |
$1$ |
\( 2 \cdot 174761 \) |
\( - 2^{77} \cdot 174761 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$1398088$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$601151936$ |
$4.150711$ |
$-29749784766896982765730316209849/26409135645209026150103252992$ |
$0.98234$ |
$5.75042$ |
$[1, 1, 0, -645535363, 10048851851085]$ |
\(y^2+xy=x^3+x^2-645535363x+10048851851085\) |
1398088.2.0.? |
$[]$ |
359550.dc1 |
359550dc4 |
359550.dc |
359550dc |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \cdot 47 \) |
\( 2^{2} \cdot 3^{9} \cdot 5^{10} \cdot 17 \cdot 47 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$95880$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$339738624$ |
$4.294250$ |
$2631913140833100999516620160001/53932500$ |
$1.05316$ |
$6.74558$ |
$[1, -1, 1, -64719000005, -6337160435020503]$ |
\(y^2+xy+y=x^3-x^2-64719000005x-6337160435020503\) |
2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 340.12.0.?, 376.12.0.?, $\ldots$ |
$[]$ |
360030.bc1 |
360030bc4 |
360030.bc |
360030bc |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 1091 \) |
\( 2 \cdot 3 \cdot 5^{3} \cdot 11 \cdot 1091 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1440120$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$24674304$ |
$2.528118$ |
$12233648382354948213504576001/9000750$ |
$0.96979$ |
$5.05505$ |
$[1, 0, 0, -48004000, -128020000750]$ |
\(y^2+xy=x^3-48004000x-128020000750\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 120.24.0.?, 48004.12.0.?, $\ldots$ |
$[]$ |
360297.v1 |
360297v6 |
360297.v |
360297v |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \cdot 19 \cdot 43 \) |
\( 3^{8} \cdot 7^{12} \cdot 19 \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$274512$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1840250880$ |
$5.105774$ |
$10861212583728923979630082266913537/865073097$ |
$1.03457$ |
$7.55295$ |
$[1, -1, 0, -2034651924153, -1117076976856888664]$ |
\(y^2+xy=x^3-x^2-2034651924153x-1117076976856888664\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0-8.n.1.6, 84.12.0.?, $\ldots$ |
$[]$ |
360297.v3 |
360297v5 |
360297.v |
360297v |
$6$ |
$8$ |
\( 3^{2} \cdot 7^{2} \cdot 19 \cdot 43 \) |
\( - 3^{8} \cdot 7^{30} \cdot 19 \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$274512$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1840250880$ |
$5.105774$ |
$-2650649113846814005259968477537/1408696794341304845090553$ |
$1.01791$ |
$6.90290$ |
$[1, -1, 0, -127149531903, -17458977183075086]$ |
\(y^2+xy=x^3-x^2-127149531903x-17458977183075086\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0-8.n.1.6, 84.12.0.?, $\ldots$ |
$[]$ |
361200.iu1 |
361200iu4 |
361200.iu |
361200iu |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43 \) |
\( 2^{16} \cdot 3 \cdot 5^{9} \cdot 7 \cdot 43 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$36120$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$113246208$ |
$3.658585$ |
$98826436705052788075008001/1806000$ |
$1.01471$ |
$6.08179$ |
$[0, 1, 0, -3852800008, -92048957056012]$ |
\(y^2=x^3+x^2-3852800008x-92048957056012\) |
2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 168.12.0.?, 172.12.0.?, $\ldots$ |
$[]$ |
380052.m1 |
380052m1 |
380052.m |
380052m |
$1$ |
$1$ |
\( 2^{2} \cdot 3^{5} \cdot 17 \cdot 23 \) |
\( - 2^{8} \cdot 3^{11} \cdot 17^{21} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$4692$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$3509339904$ |
$5.502693$ |
$-140364106723253635814915188455024/1589114479999200856259025991$ |
$1.06155$ |
$7.13501$ |
$[0, 0, 0, -386101990359, -93241291095147618]$ |
\(y^2=x^3-386101990359x-93241291095147618\) |
4692.2.0.? |
$[]$ |
386860.e1 |
386860e2 |
386860.e |
386860e |
$2$ |
$2$ |
\( 2^{2} \cdot 5 \cdot 23 \cdot 29^{2} \) |
\( 2^{8} \cdot 5^{3} \cdot 23^{3} \cdot 29^{16} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$13340$ |
$12$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$1415232000$ |
$4.833710$ |
$1443000217667215837487184/639843113445443195875$ |
$1.06279$ |
$6.32511$ |
$[0, 0, 0, -12571590103, -262326061712898]$ |
\(y^2=x^3-12571590103x-262326061712898\) |
2.3.0.a.1, 116.6.0.?, 460.6.0.?, 13340.12.0.? |
$[]$ |
396942.j2 |
396942j6 |
396942.j |
396942j |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 727 \) |
\( 2 \cdot 3^{12} \cdot 7 \cdot 13 \cdot 727^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.177 |
2B |
$1058512$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1144258560$ |
$4.633110$ |
$28123252977982714556912518905062497/7547475840053709870107653841622$ |
$1.00814$ |
$6.15302$ |
$[1, 1, 1, -6335495894, 142133468187485]$ |
\(y^2+xy+y=x^3+x^2-6335495894x+142133468187485\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 728.96.0.?, 11632.96.0.?, $\ldots$ |
$[]$ |
396942.j5 |
396942j5 |
396942.j |
396942j |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 727 \) |
\( - 2 \cdot 3^{48} \cdot 7 \cdot 13 \cdot 727^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$1058512$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1144258560$ |
$4.633110$ |
$-17134464565604420040179238142555297/7672915867521695839334163326358$ |
$1.00676$ |
$6.15904$ |
$[1, 1, 1, -5370923194, 201776277773117]$ |
\(y^2+xy+y=x^3+x^2-5370923194x+201776277773117\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 728.48.0.?, $\ldots$ |
$[]$ |
412830.t1 |
412830t1 |
412830.t |
412830t |
$1$ |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \cdot 11 \cdot 139 \) |
\( - 2^{41} \cdot 3^{11} \cdot 5^{2} \cdot 11^{3} \cdot 139 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$36696$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1263928320$ |
$4.827820$ |
$-8218804328669112404412122444831403/10170977337160499200$ |
$1.02802$ |
$6.97378$ |
$[1, -1, 0, -236123698389, -44162830286268427]$ |
\(y^2+xy=x^3-x^2-236123698389x-44162830286268427\) |
36696.2.0.? |
$[]$ |
416955.ca1 |
416955ca4 |
416955.ca |
416955ca |
$6$ |
$8$ |
\( 3 \cdot 5 \cdot 7 \cdot 11 \cdot 19^{2} \) |
\( 3 \cdot 5^{2} \cdot 7 \cdot 11 \cdot 19^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.4 |
2B |
$70224$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$112066560$ |
$3.665676$ |
$152018859433705106722387201/2084775$ |
$0.98947$ |
$6.02382$ |
$[1, 0, 1, -4013886808, -97880747966557]$ |
\(y^2+xy+y=x^3-4013886808x-97880747966557\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.8, $\ldots$ |
$[]$ |
421590.bo3 |
421590bo1 |
421590.bo |
421590bo |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 23 \cdot 47 \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{5} \cdot 13 \cdot 23 \cdot 47^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.12 |
2B |
$562120$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$312115200$ |
$3.977173$ |
$665536502121401514336079243593102769/13969384650000$ |
$1.00974$ |
$6.36869$ |
$[1, 0, 0, -18189302931, -944219346505839]$ |
\(y^2+xy=x^3-18189302931x-944219346505839\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 188.12.0.?, 376.24.0.?, $\ldots$ |
$[]$ |
421590.bo4 |
421590bo4 |
421590.bo |
421590bo |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 23 \cdot 47 \) |
\( - 2 \cdot 3^{8} \cdot 5^{5} \cdot 13 \cdot 23 \cdot 47^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.7 |
2B |
$562120$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1248460800$ |
$4.670319$ |
$-664511383209578148446989492702082449/1424608524266660468312006868750$ |
$1.00976$ |
$6.36885$ |
$[1, 0, 0, -18179959201, -945237874744345]$ |
\(y^2+xy=x^3-18179959201x-945237874744345\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 376.24.0.?, 5980.12.0.?, $\ldots$ |
$[]$ |
436170.bl1 |
436170bl4 |
436170.bl |
436170bl |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 31 \cdot 67 \) |
\( 2 \cdot 3^{5} \cdot 5^{8} \cdot 7^{5} \cdot 31 \cdot 67 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$348936$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$699596800$ |
$4.391342$ |
$81923555729002031877505517079537184849/6627092013281250$ |
$1.01824$ |
$6.72265$ |
$[1, 0, 0, -90481896301, -10475890902644545]$ |
\(y^2+xy=x^3-90481896301x-10475890902644545\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 868.12.0.?, 1608.24.0.?, $\ldots$ |
$[]$ |
439920.eh4 |
439920eh4 |
439920.eh |
439920eh |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 47 \) |
\( - 2^{13} \cdot 3^{15} \cdot 5 \cdot 13^{2} \cdot 47^{12} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$5640$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$1$ |
$2760376320$ |
$5.215103$ |
$-11597845094944722710152295329/3865024865836504922724749070$ |
$1.06182$ |
$6.60962$ |
$[0, 0, 0, -6790686627, -5173146359135966]$ |
\(y^2=x^3-6790686627x-5173146359135966\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.2, 120.24.0.?, $\ldots$ |
$[]$ |
466032.bl1 |
466032bl4 |
466032.bl |
466032bl |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \cdot 73 \) |
\( 2^{26} \cdot 3^{3} \cdot 7 \cdot 19 \cdot 73 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.46 |
2B |
$466032$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$1$ |
$974389248$ |
$4.650269$ |
$1329212784039368249494298857429794817/4294950912$ |
$1.03600$ |
$7.01006$ |
$[0, 1, 0, -366502477824, -85401226430081100]$ |
\(y^2=x^3+x^2-366502477824x-85401226430081100\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.h.1.6, 456.48.0.?, $\ldots$ |
$[]$ |
484590.n1 |
484590n4 |
484590.n |
484590n |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 29 \cdot 557 \) |
\( 2 \cdot 3 \cdot 5 \cdot 29 \cdot 557 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1938360$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$3768320$ |
$1.861645$ |
$1909164058393092684433921/484590$ |
$1.00213$ |
$4.27076$ |
$[1, 0, 0, -2584480, -1599434158]$ |
\(y^2+xy=x^3-2584480x-1599434158\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 696.24.0.?, 11140.12.0.?, $\ldots$ |
$[]$ |
487110.bc1 |
487110bc6 |
487110.bc |
487110bc |
$6$ |
$8$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 1249 \) |
\( 2^{2} \cdot 3 \cdot 5^{4} \cdot 13 \cdot 1249^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$779376$ |
$192$ |
$1$ |
$1$ |
$256$ |
$2$ |
$0$ |
$1656750080$ |
$4.793587$ |
$59034837655342327741563176897817674880001/152100097500$ |
$1.02792$ |
$7.16839$ |
$[1, 0, 0, -811200520000, -281216338000097500]$ |
\(y^2+xy=x^3-811200520000x-281216338000097500\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 156.24.0.?, $\ldots$ |
$[]$ |
497100.b1 |
497100b1 |
497100.b |
497100b |
$1$ |
$1$ |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 1657 \) |
\( - 2^{8} \cdot 3^{24} \cdot 5^{10} \cdot 1657 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6628$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$434229120$ |
$4.077988$ |
$-7380039411600791735592400/467985741949017$ |
$0.98804$ |
$6.01533$ |
$[0, -1, 0, -5505012708, -157210140926088]$ |
\(y^2=x^3-x^2-5505012708x-157210140926088\) |
6628.2.0.? |
$[]$ |
498270.y1 |
498270y4 |
498270.y |
498270y |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 977 \) |
\( 2^{5} \cdot 3 \cdot 5^{5} \cdot 17^{3} \cdot 977 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$1993080$ |
$48$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$7431782400$ |
$5.323601$ |
$50096529850862518508552454162800640230400001/1440000300000$ |
$1.03766$ |
$7.67004$ |
$[1, 0, 0, -7680001600000, -8192003200000300000]$ |
\(y^2+xy=x^3-7680001600000x-8192003200000300000\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 120.24.0.?, 66436.12.0.?, $\ldots$ |
$[]$ |
8467200.bad1 |
- |
8467200.bad |
- |
$1$ |
$1$ |
\( 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{11} \cdot 5^{15} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$120$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
$18632540160$ |
$4.761520$ |
$-29372519473126518336/1953125$ |
$1.14221$ |
$5.55681$ |
$[0, 0, 0, -141515224200, -20490514307424000]$ |
\(y^2=x^3-141515224200x-20490514307424000\) |
120.2.0.? |
$[]$ |
25897769.a1 |
- |
25897769.a |
- |
$1$ |
$1$ |
\( 25897769 \) |
\( -25897769 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$103591076$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
|
$1.926720$ |
$-2406211360520771614293657/25897769$ |
$0.86276$ |
$3.28888$ |
$[1, -1, 0, -2791708, -1794668683]$ |
\(y^2+xy=x^3-x^2-2791708x-1794668683\) |
103591076.2.0.? |
$[]$ |
184067431.a1 |
- |
184067431.a |
- |
$1$ |
$1$ |
\( 184067431 \) |
\( 184067431 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$736269724$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
|
$3.213997$ |
$91241991405713191602951317973529/184067431$ |
$0.89583$ |
$3.86694$ |
$[1, 0, 1, -937901034, -11055711710607]$ |
\(y^2+xy+y=x^3-937901034x-11055711710607\) |
736269724.2.0.? |
$[]$ |
187712299.a1 |
- |
187712299.a |
- |
$1$ |
$1$ |
\( 187712299 \) |
\( -187712299 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$375424598$ |
$2$ |
$0$ |
$1$ |
$256$ |
$2$ |
$0$ |
|
$1.452999$ |
$-1601504996217813708553/187712299$ |
$0.79352$ |
$2.56295$ |
$[1, 1, 0, -243744, -46419625]$ |
\(y^2+xy=x^3+x^2-243744x-46419625\) |
375424598.2.0.? |
$[]$ |