| 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 |
| 136367.a1 |
136367a1 |
136367.a |
136367a |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{2} \cdot 11^{7} \cdot 23 \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$506$ |
$2$ |
$0$ |
$0.900510408$ |
$1$ |
|
$12$ |
$152640$ |
$0.892007$ |
$196661248/253$ |
$0.75892$ |
$3.16128$ |
$[0, -1, 1, -5364, 152844]$ |
\(y^2+y=x^3-x^2-5364x+152844\) |
506.2.0.? |
$[(37, 60), (157/2, 277/2)]$ |
| 136367.b1 |
136367b1 |
136367.b |
136367b |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{8} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$506$ |
$2$ |
$0$ |
$1.865850000$ |
$1$ |
|
$2$ |
$1068480$ |
$1.864962$ |
$196661248/253$ |
$0.75892$ |
$4.14880$ |
$[0, 1, 1, -262852, -51899886]$ |
\(y^2+y=x^3+x^2-262852x-51899886\) |
506.2.0.? |
$[(1437, 50396)]$ |
| 136367.c1 |
136367c2 |
136367.c |
136367c |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{3} \cdot 11^{7} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1105920$ |
$1.639727$ |
$11961853903/3078251$ |
$0.84871$ |
$3.67332$ |
$[1, 0, 0, -40356, -2328677]$ |
\(y^2+xy=x^3-40356x-2328677\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.d.1, 154.6.0.?, 308.12.0.? |
$[]$ |
| 136367.c2 |
136367c1 |
136367.c |
136367c |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{3} \cdot 11^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$552960$ |
$1.293154$ |
$43986977/64009$ |
$0.79931$ |
$3.23431$ |
$[1, 0, 0, 6229, -232352]$ |
\(y^2+xy=x^3+6229x-232352\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.? |
$[]$ |
| 136367.d1 |
136367d1 |
136367.d |
136367d |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{9} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$27095040$ |
$3.507683$ |
$4505721246665691247/253$ |
$0.97416$ |
$6.33103$ |
$[1, 1, 1, -1428103531, 20771851644270]$ |
\(y^2+xy+y=x^3+x^2-1428103531x+20771851644270\) |
7084.2.0.? |
$[]$ |
| 136367.e1 |
136367e2 |
136367.e |
136367e |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{3} \cdot 11^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.27 |
2B |
$14168$ |
$48$ |
$1$ |
$1$ |
$4$ |
$2$ |
$0$ |
$19169280$ |
$3.090664$ |
$4399901392374538640127/64009$ |
$1.04974$ |
$5.92577$ |
$[1, -1, 1, -289149972, -1892414450440]$ |
\(y^2+xy+y=x^3-x^2-289149972x-1892414450440\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.l.1, 56.24.0.cb.1, $\ldots$ |
$[]$ |
| 136367.e2 |
136367e1 |
136367.e |
136367e |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{3} \cdot 11^{10} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.11 |
2B |
$14168$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$9584640$ |
$2.744091$ |
$-1074191725926252207/4097152081$ |
$1.02189$ |
$5.22225$ |
$[1, -1, 1, -18071857, -29565644160]$ |
\(y^2+xy+y=x^3-x^2-18071857x-29565644160\) |
2.3.0.a.1, 4.12.0.f.1, 14.6.0.b.1, 28.24.0.g.1, 2024.24.0.?, $\ldots$ |
$[]$ |
| 136367.f1 |
136367f2 |
136367.f |
136367f |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{9} \cdot 11^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.27 |
2B |
$14168$ |
$48$ |
$1$ |
$1$ |
$4$ |
$2$ |
$0$ |
$134184960$ |
$4.063622$ |
$4399901392374538640127/64009$ |
$1.04974$ |
$6.91328$ |
$[1, -1, 1, -14168348613, 649126493198054]$ |
\(y^2+xy+y=x^3-x^2-14168348613x+649126493198054\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.l.1, 56.24.0.cb.1, $\ldots$ |
$[]$ |
| 136367.f2 |
136367f1 |
136367.f |
136367f |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{9} \cdot 11^{10} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.11 |
2B |
$14168$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$67092480$ |
$3.717045$ |
$-1074191725926252207/4097152081$ |
$1.02189$ |
$6.20976$ |
$[1, -1, 1, -885520978, 10142786988744]$ |
\(y^2+xy+y=x^3-x^2-885520978x+10142786988744\) |
2.3.0.a.1, 4.12.0.f.1, 14.6.0.b.1, 28.24.0.g.1, 2024.24.0.?, $\ldots$ |
$[]$ |
| 136367.g1 |
136367g1 |
136367.g |
136367g |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{3} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$3870720$ |
$2.534729$ |
$4505721246665691247/253$ |
$0.97416$ |
$5.34352$ |
$[1, 0, 0, -29144970, -60563497807]$ |
\(y^2+xy=x^3-29144970x-60563497807\) |
7084.2.0.? |
$[]$ |
| 136367.h1 |
136367h2 |
136367.h |
136367h |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{9} \cdot 11^{7} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$7741440$ |
$2.612682$ |
$11961853903/3078251$ |
$0.84871$ |
$4.66084$ |
$[1, 1, 1, -1977445, 796758766]$ |
\(y^2+xy+y=x^3+x^2-1977445x+796758766\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.d.1, 154.6.0.?, 308.12.0.? |
$[]$ |
| 136367.h2 |
136367h1 |
136367.h |
136367h |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{9} \cdot 11^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3870720$ |
$2.266109$ |
$43986977/64009$ |
$0.79931$ |
$4.22183$ |
$[1, 1, 1, 305220, 80001956]$ |
\(y^2+xy+y=x^3+x^2+305220x+80001956\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.? |
$[]$ |
| 136367.i1 |
136367i1 |
136367.i |
136367i |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{7} \cdot 11^{7} \cdot 23^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$5.770799535$ |
$1$ |
|
$0$ |
$7372800$ |
$2.547810$ |
$1794942305577/495598411$ |
$0.88792$ |
$4.59091$ |
$[1, -1, 1, -1501149, -511526606]$ |
\(y^2+xy+y=x^3-x^2-1501149x-511526606\) |
7084.2.0.? |
$[(34171/3, 5895517/3)]$ |
| 136367.j1 |
136367j1 |
136367.j |
136367j |
$2$ |
$3$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{9} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$10626$ |
$16$ |
$0$ |
$2.115541378$ |
$1$ |
|
$2$ |
$829440$ |
$1.857529$ |
$-799178752/86779$ |
$0.79027$ |
$3.95276$ |
$[0, -1, 1, -114627, 16316992]$ |
\(y^2+y=x^3-x^2-114627x+16316992\) |
3.4.0.a.1, 138.8.0.?, 231.8.0.?, 3542.2.0.?, 10626.16.0.? |
$[(152, 1543)]$ |
| 136367.j2 |
136367j2 |
136367.j |
136367j |
$2$ |
$3$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{7} \cdot 11^{9} \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$10626$ |
$16$ |
$0$ |
$6.346624136$ |
$1$ |
|
$2$ |
$2488320$ |
$2.406834$ |
$194305753088/113359939$ |
$0.95045$ |
$4.40286$ |
$[0, -1, 1, 715433, -21243223]$ |
\(y^2+y=x^3-x^2+715433x-21243223\) |
3.4.0.a.1, 138.8.0.?, 231.8.0.?, 3542.2.0.?, 10626.16.0.? |
$[(6081, 478705)]$ |
| 136367.k1 |
136367k1 |
136367.k |
136367k |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{3} \cdot 11^{13} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2795520$ |
$2.039669$ |
$950152003191/448204933$ |
$0.93247$ |
$4.04335$ |
$[1, -1, 0, -173476, -11914127]$ |
\(y^2+xy=x^3-x^2-173476x-11914127\) |
7084.2.0.? |
$[]$ |
| 136367.l1 |
136367l1 |
136367.l |
136367l |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{3} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$2.262136273$ |
$1$ |
|
$0$ |
$184320$ |
$1.142380$ |
$1201157047/253$ |
$0.87938$ |
$3.47892$ |
$[1, 1, 0, -18757, -996442]$ |
\(y^2+xy=x^3+x^2-18757x-996442\) |
7084.2.0.? |
$[(-2006/5, 5862/5)]$ |
| 136367.m1 |
136367m3 |
136367.m |
136367m |
$4$ |
$4$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{10} \cdot 11^{6} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$14168$ |
$48$ |
$0$ |
$3.811205202$ |
$1$ |
|
$0$ |
$1228800$ |
$2.066269$ |
$209267191953/55223$ |
$0.94092$ |
$4.40914$ |
$[1, -1, 0, -733343, 241846226]$ |
\(y^2+xy=x^3-x^2-733343x+241846226\) |
2.3.0.a.1, 4.6.0.c.1, 56.12.0.z.1, 88.12.0.?, 92.12.0.?, $\ldots$ |
$[(631/2, 90607/2)]$ |
| 136367.m2 |
136367m2 |
136367.m |
136367m |
$4$ |
$4$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{8} \cdot 11^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$7084$ |
$48$ |
$0$ |
$7.622410405$ |
$1$ |
|
$2$ |
$614400$ |
$1.719696$ |
$72511713/25921$ |
$0.92625$ |
$3.73524$ |
$[1, -1, 0, -51508, 2794875]$ |
\(y^2+xy=x^3-x^2-51508x+2794875\) |
2.6.0.a.1, 28.12.0.b.1, 44.12.0-2.a.1.1, 92.12.0.?, 308.24.0.?, $\ldots$ |
$[(1689/8, 610497/8)]$ |
| 136367.m3 |
136367m1 |
136367.m |
136367m |
$4$ |
$4$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{7} \cdot 11^{6} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$14168$ |
$48$ |
$0$ |
$15.24482081$ |
$1$ |
|
$1$ |
$307200$ |
$1.373121$ |
$5545233/161$ |
$0.79467$ |
$3.51780$ |
$[1, -1, 0, -21863, -1207200]$ |
\(y^2+xy=x^3-x^2-21863x-1207200\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.2, 56.12.0.z.1, 184.12.0.?, $\ldots$ |
$[(37098912/323, 195883192992/323)]$ |
| 136367.m4 |
136367m4 |
136367.m |
136367m |
$4$ |
$4$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{7} \cdot 11^{6} \cdot 23^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$14168$ |
$48$ |
$0$ |
$3.811205202$ |
$1$ |
|
$2$ |
$1228800$ |
$2.066269$ |
$2014698447/1958887$ |
$0.97932$ |
$4.01642$ |
$[1, -1, 0, 156007, 19520584]$ |
\(y^2+xy=x^3-x^2+156007x+19520584\) |
2.3.0.a.1, 4.6.0.c.1, 14.6.0.b.1, 28.12.0.g.1, 44.12.0-4.c.1.1, $\ldots$ |
$[(5448, 400448)]$ |
| 136367.n1 |
136367n1 |
136367.n |
136367n |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{9} \cdot 11^{7} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$2.119217964$ |
$1$ |
|
$2$ |
$1290240$ |
$2.115334$ |
$1201157047/253$ |
$0.87938$ |
$4.46643$ |
$[1, 0, 1, -919119, 339022275]$ |
\(y^2+xy+y=x^3-919119x+339022275\) |
7084.2.0.? |
$[(543, 71)]$ |
| 136367.o1 |
136367o1 |
136367.o |
136367o |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{7} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$368640$ |
$1.541273$ |
$24137569/1771$ |
$0.82777$ |
$3.64220$ |
$[1, 0, 1, -35698, -2428835]$ |
\(y^2+xy+y=x^3-35698x-2428835\) |
7084.2.0.? |
$[]$ |
| 136367.p1 |
136367p2 |
136367.p |
136367p |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{8} \cdot 11^{10} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$644$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$4608000$ |
$2.285511$ |
$128100283921/16500407$ |
$1.04025$ |
$4.36763$ |
$[1, 1, 0, -622668, -167007595]$ |
\(y^2+xy=x^3+x^2-622668x-167007595\) |
2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.? |
$[]$ |
| 136367.p2 |
136367p1 |
136367.p |
136367p |
$2$ |
$2$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{7} \cdot 11^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$644$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$2304000$ |
$1.938940$ |
$109902239/448063$ |
$0.85315$ |
$3.92259$ |
$[1, 1, 0, 59167, -13594720]$ |
\(y^2+xy=x^3+x^2+59167x-13594720\) |
2.3.0.a.1, 14.6.0.b.1, 92.6.0.?, 644.12.0.? |
$[]$ |
| 136367.q1 |
136367q1 |
136367.q |
136367q |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( 7^{9} \cdot 11^{13} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$7084$ |
$2$ |
$0$ |
$1$ |
$16$ |
$2$ |
$0$ |
$19568640$ |
$3.012627$ |
$950152003191/448204933$ |
$0.93247$ |
$5.03087$ |
$[1, -1, 0, -8500333, 4103546222]$ |
\(y^2+xy=x^3-x^2-8500333x+4103546222\) |
7084.2.0.? |
$[]$ |
| 136367.r1 |
136367r1 |
136367.r |
136367r |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{3} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3542$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$161280$ |
$0.830611$ |
$110592/253$ |
$0.59685$ |
$2.78451$ |
$[0, 0, 1, 847, -16305]$ |
\(y^2+y=x^3+847x-16305\) |
3542.2.0.? |
$[]$ |
| 136367.s1 |
136367s1 |
136367.s |
136367s |
$1$ |
$1$ |
\( 7^{2} \cdot 11^{2} \cdot 23 \) |
\( - 7^{9} \cdot 11^{7} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3542$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1128960$ |
$1.803566$ |
$110592/253$ |
$0.59685$ |
$3.77202$ |
$[0, 0, 1, 41503, 5592529]$ |
\(y^2+y=x^3+41503x+5592529\) |
3542.2.0.? |
$[]$ |
