| 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 |
| 2002.b4 |
2002b4 |
2002.b |
2002b |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$8008$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$768$ |
$0.459628$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.76812$ |
$[1, -1, 0, 154, -1960]$ |
\(y^2+xy=x^3-x^2+154x-1960\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 52.24.0-52.h.1.2, 616.24.0.?, 8008.48.0.? |
$[]$ |
| 14014.b4 |
14014d4 |
14014.b |
14014d |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$0.814930090$ |
$1$ |
|
$6$ |
$36864$ |
$1.432583$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.22299$ |
$[1, -1, 0, 7537, 657201]$ |
\(y^2+xy=x^3-x^2+7537x+657201\) |
2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 52.12.0.h.1, 88.12.0.?, $\ldots$ |
$[(-40, 559)]$ |
| 16016.f4 |
16016g4 |
16016.f |
16016g |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{14} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$8008$ |
$48$ |
$0$ |
$4.931640385$ |
$1$ |
|
$1$ |
$18432$ |
$1.152775$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.81793$ |
$[0, 0, 0, 2461, 122978]$ |
\(y^2=x^3+2461x+122978\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 52.24.0-52.h.1.1, 616.24.0.?, 8008.48.0.? |
$[(2719/3, 143990/3)]$ |
| 18018.z4 |
18018bo4 |
18018.z |
18018bo |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 3^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24024$ |
$48$ |
$0$ |
$1.369859644$ |
$1$ |
|
$4$ |
$24576$ |
$1.008934$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.59589$ |
$[1, -1, 1, 1384, 51535]$ |
\(y^2+xy+y=x^3-x^2+1384x+51535\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 52.12.0.h.1, 156.24.0.?, $\ldots$ |
$[(5, 239)]$ |
| 22022.o4 |
22022m3 |
22022.o |
22022m |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \cdot 13 \) |
\( - 2^{2} \cdot 7^{4} \cdot 11^{10} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$6.540526919$ |
$1$ |
|
$0$ |
$92160$ |
$1.658575$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.30331$ |
$[1, -1, 1, 18611, 2552905]$ |
\(y^2+xy+y=x^3-x^2+18611x+2552905\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.2, 52.12.0.h.1, 56.12.0-4.c.1.5, $\ldots$ |
$[(3071/5, 315366/5)]$ |
| 26026.l4 |
26026i3 |
26026.l |
26026i |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11 \cdot 13^{2} \) |
\( - 2^{2} \cdot 7^{4} \cdot 11^{4} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$8008$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$129024$ |
$1.742102$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.33119$ |
$[1, -1, 1, 25994, -4228103]$ |
\(y^2+xy+y=x^3-x^2+25994x-4228103\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 52.24.0-52.h.1.1, 616.24.0.?, 8008.48.0.? |
$[]$ |
| 50050.bw4 |
50050bj3 |
50050.bw |
50050bj |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 5^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$40040$ |
$48$ |
$0$ |
$3.028317858$ |
$1$ |
|
$2$ |
$98304$ |
$1.264347$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.53963$ |
$[1, -1, 1, 3845, -241153]$ |
\(y^2+xy+y=x^3-x^2+3845x-241153\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 52.12.0.h.1, 260.24.0.?, $\ldots$ |
$[(99, 1000)]$ |
| 64064.s4 |
64064bb3 |
64064.s |
64064bb |
$4$ |
$4$ |
\( 2^{6} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{20} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$8008$ |
$48$ |
$0$ |
$1.209207503$ |
$1$ |
|
$5$ |
$147456$ |
$1.499348$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.71548$ |
$[0, 0, 0, 9844, 983824]$ |
\(y^2=x^3+9844x+983824\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 52.12.0.h.1, 104.24.0.?, $\ldots$ |
$[(130, 2112)]$ |
| 64064.u4 |
64064k3 |
64064.u |
64064k |
$4$ |
$4$ |
\( 2^{6} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{20} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$8008$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$147456$ |
$1.499348$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.71548$ |
$[0, 0, 0, 9844, -983824]$ |
\(y^2=x^3+9844x-983824\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0.h.1, 104.24.0.?, $\ldots$ |
$[]$ |
| 112112.v4 |
112112z3 |
112112.v |
112112z |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{14} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$6.919138690$ |
$1$ |
|
$1$ |
$884736$ |
$2.125729$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.18311$ |
$[0, 0, 0, 120589, -42181454]$ |
\(y^2=x^3+120589x-42181454\) |
2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 52.12.0.h.1, 88.12.0.?, $\ldots$ |
$[(15751/5, 2106126/5)]$ |
| 126126.fj4 |
126126et3 |
126126.fj |
126126et |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 3^{6} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24024$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$1179648$ |
$1.981890$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.99420$ |
$[1, -1, 1, 67831, -17812259]$ |
\(y^2+xy+y=x^3-x^2+67831x-17812259\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 84.12.0.?, 264.12.0.?, $\ldots$ |
$[]$ |
| 144144.x4 |
144144m3 |
144144.x |
144144m |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{14} \cdot 3^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24024$ |
$48$ |
$0$ |
$2.969821766$ |
$1$ |
|
$5$ |
$589824$ |
$1.702082$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.66663$ |
$[0, 0, 0, 22149, -3320406]$ |
\(y^2=x^3+22149x-3320406\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 52.12.0.h.1, 156.24.0.?, $\ldots$ |
$[(151, 1862)]$ |
| 154154.cc4 |
154154p3 |
154154.cc |
154154p |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11^{2} \cdot 13 \) |
\( - 2^{2} \cdot 7^{10} \cdot 11^{10} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$8008$ |
$48$ |
$0$ |
$10.97524225$ |
$1$ |
|
$0$ |
$4423680$ |
$2.631531$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.57970$ |
$[1, -1, 1, 911954, -877470415]$ |
\(y^2+xy+y=x^3-x^2+911954x-877470415\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 52.12.0.h.1, 104.24.0.?, $\ldots$ |
$[(3722769/23, 7196557223/23)]$ |
| 176176.ce4 |
176176bf3 |
176176.ce |
176176bf |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \cdot 11^{2} \cdot 13 \) |
\( - 2^{14} \cdot 7^{4} \cdot 11^{10} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$2211840$ |
$2.351723$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.25110$ |
$[0, 0, 0, 297781, -163683718]$ |
\(y^2=x^3+297781x-163683718\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.1, 52.12.0.h.1, 56.12.0-4.c.1.5, $\ldots$ |
$[]$ |
| 182182.bq4 |
182182q4 |
182182.bq |
182182q |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \cdot 13^{2} \) |
\( - 2^{2} \cdot 7^{10} \cdot 11^{4} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$13.81671630$ |
$1$ |
|
$0$ |
$6193152$ |
$2.715057$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.59929$ |
$[1, -1, 1, 1273721, 1447691795]$ |
\(y^2+xy+y=x^3-x^2+1273721x+1447691795\) |
2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 52.12.0.h.1, 88.12.0.?, $\ldots$ |
$[(20259579/185, 308878351472/185)]$ |
| 198198.i4 |
198198cv3 |
198198.i |
198198cv |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 13 \) |
\( - 2^{2} \cdot 3^{6} \cdot 7^{4} \cdot 11^{10} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24024$ |
$48$ |
$0$ |
$4.306425679$ |
$1$ |
|
$2$ |
$2949120$ |
$2.207882$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.06853$ |
$[1, -1, 0, 167502, -69095944]$ |
\(y^2+xy=x^3-x^2+167502x-69095944\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 132.12.0.?, 168.12.0.?, $\ldots$ |
$[(1273, 46330)]$ |
| 208208.bc4 |
208208p4 |
208208.bc |
208208p |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \cdot 11 \cdot 13^{2} \) |
\( - 2^{14} \cdot 7^{4} \cdot 11^{4} \cdot 13^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$8008$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$3096576$ |
$2.435249$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.27496$ |
$[0, 0, 0, 415909, 270182666]$ |
\(y^2=x^3+415909x+270182666\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 52.24.0-52.h.1.2, 616.24.0.?, 8008.48.0.? |
$[]$ |
| 234234.cd4 |
234234cd4 |
234234.cd |
234234cd |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 11 \cdot 13^{2} \) |
\( - 2^{2} \cdot 3^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$24024$ |
$48$ |
$0$ |
$1.129036300$ |
$1$ |
|
$6$ |
$4128768$ |
$2.291409$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.09463$ |
$[1, -1, 0, 233949, 113924825]$ |
\(y^2+xy=x^3-x^2+233949x+113924825\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 52.12.0.h.1, 156.24.0.?, $\ldots$ |
$[(-172, 8367)]$ |
| 286286.v4 |
286286v4 |
286286.v |
286286v |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \cdot 13^{2} \) |
\( - 2^{2} \cdot 7^{4} \cdot 11^{10} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$1.493589972$ |
$1$ |
|
$6$ |
$15482880$ |
$2.941051$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.64967$ |
$[1, -1, 0, 3145312, 5618168804]$ |
\(y^2+xy=x^3-x^2+3145312x+5618168804\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.1, 52.12.0.h.1, 56.12.0-4.c.1.3, $\ldots$ |
$[(1114, 101930)]$ |
| 350350.fs4 |
350350fs4 |
350350.fs |
350350fs |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 5^{6} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$40040$ |
$48$ |
$0$ |
$4.472525955$ |
$1$ |
|
$2$ |
$4718592$ |
$2.237301$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.91464$ |
$[1, -1, 1, 188420, 82338547]$ |
\(y^2+xy+y=x^3-x^2+188420x+82338547\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 140.12.0.?, 440.12.0.?, $\ldots$ |
$[(6509, 523095)]$ |
| 400400.dc4 |
400400dc4 |
400400.dc |
400400dc |
$4$ |
$4$ |
\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{14} \cdot 5^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$40040$ |
$48$ |
$0$ |
$3.725998077$ |
$1$ |
|
$3$ |
$2359296$ |
$1.957495$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.61384$ |
$[0, 0, 0, 61525, 15372250]$ |
\(y^2=x^3+61525x+15372250\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 52.12.0.h.1, 260.24.0.?, $\ldots$ |
$[(55, 4350)]$ |
| 448448.cj4 |
448448cj4 |
448448.cj |
448448cj |
$4$ |
$4$ |
\( 2^{6} \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{20} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$11.75567600$ |
$1$ |
|
$1$ |
$7077888$ |
$2.472305$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.05708$ |
$[0, 0, 0, 482356, 337451632]$ |
\(y^2=x^3+482356x+337451632\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 56.12.0-4.c.1.1, 88.12.0.?, $\ldots$ |
$[(6054601/20, 14914409349/20)]$ |
| 448448.co4 |
448448co3 |
448448.co |
448448co |
$4$ |
$4$ |
\( 2^{6} \cdot 7^{2} \cdot 11 \cdot 13 \) |
\( - 2^{20} \cdot 7^{10} \cdot 11^{4} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8008$ |
$48$ |
$0$ |
$5.981346186$ |
$1$ |
|
$1$ |
$7077888$ |
$2.472305$ |
$402437650887/1827958132$ |
$0.92555$ |
$4.05708$ |
$[0, 0, 0, 482356, -337451632]$ |
\(y^2=x^3+482356x-337451632\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 56.12.0-4.c.1.2, 88.12.0.?, $\ldots$ |
$[(22786/3, 3531968/3)]$ |
| 450450.r4 |
450450r4 |
450450.r |
450450r |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \) |
\( - 2^{2} \cdot 3^{6} \cdot 5^{6} \cdot 7^{4} \cdot 11^{4} \cdot 13 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$120120$ |
$48$ |
$0$ |
$5.251773849$ |
$1$ |
|
$12$ |
$3145728$ |
$1.813652$ |
$402437650887/1827958132$ |
$0.92555$ |
$3.44855$ |
$[1, -1, 0, 34608, 6476516]$ |
\(y^2+xy=x^3-x^2+34608x+6476516\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0.h.1, 60.12.0-4.c.1.2, 616.12.0.?, $\ldots$ |
$[(145, 3739), (-17, 2434)]$ |
