| 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 |
| 1323.a1 |
1323s1 |
1323.a |
1323s |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{9} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$126$ |
$36$ |
$3$ |
$0.084579310$ |
$1$ |
|
$10$ |
$576$ |
$0.132956$ |
$110592$ |
$1.11269$ |
$3.80358$ |
$[0, 0, 1, -189, 992]$ |
\(y^2+y=x^3-189x+992\) |
3.3.0.a.1, 6.6.0.c.1, 9.9.0.a.1, 18.18.1.b.1, 21.6.0.a.1, $\ldots$ |
$[(0, 31)]$ |
| 1323.b1 |
1323r1 |
1323.b |
1323r |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{5} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.254457554$ |
$1$ |
|
$6$ |
$576$ |
$0.282693$ |
$12288/7$ |
$1.11269$ |
$3.69869$ |
$[0, 0, 1, -147, -86]$ |
\(y^2+y=x^3-147x-86\) |
42.2.0.a.1 |
$[(-7, 24)]$ |
| 1323.c1 |
1323j1 |
1323.c |
1323j |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{9} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$126$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$4032$ |
$1.105911$ |
$110592$ |
$1.11269$ |
$5.42796$ |
$[0, 0, 1, -9261, -340342]$ |
\(y^2+y=x^3-9261x-340342\) |
3.3.0.a.1, 6.6.0.c.1, 9.9.0.a.1, 18.18.1.b.1, 21.6.0.a.1, $\ldots$ |
$[]$ |
| 1323.d1 |
1323g1 |
1323.d |
1323g |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{11} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3780$ |
$1.311968$ |
$-147$ |
$1.20397$ |
$5.43713$ |
$[1, -1, 1, -4052, -353510]$ |
\(y^2+xy+y=x^3-x^2-4052x-353510\) |
6.2.0.a.1 |
$[]$ |
| 1323.e1 |
1323p1 |
1323.e |
1323p |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$84$ |
$12$ |
$1$ |
$0.245200968$ |
$1$ |
|
$4$ |
$96$ |
$-0.558972$ |
$27$ |
$1.11269$ |
$2.30569$ |
$[1, -1, 1, 1, 4]$ |
\(y^2+xy+y=x^3-x^2+x+4\) |
3.3.0.a.1, 12.6.0.h.1, 21.6.0.a.1, 84.12.1.? |
$[(2, 2)]$ |
| 1323.f1 |
1323f1 |
1323.f |
1323f |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$84$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$672$ |
$0.413983$ |
$27$ |
$1.11269$ |
$3.93007$ |
$[1, -1, 1, 64, -1592]$ |
\(y^2+xy+y=x^3-x^2+64x-1592\) |
3.3.0.a.1, 12.6.0.h.1, 21.6.0.a.1, 84.12.1.? |
$[]$ |
| 1323.g1 |
1323l1 |
1323.g |
1323l |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{11} \cdot 7^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$540$ |
$0.339013$ |
$-147$ |
$1.20397$ |
$3.81275$ |
$[1, -1, 1, -83, 1054]$ |
\(y^2+xy+y=x^3-x^2-83x+1054\) |
6.2.0.a.1 |
$[]$ |
| 1323.h1 |
1323n2 |
1323.h |
1323n |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{5} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$126$ |
$144$ |
$3$ |
$2.597259346$ |
$1$ |
|
$0$ |
$1728$ |
$0.982284$ |
$35184082944/7$ |
$1.08638$ |
$5.76716$ |
$[0, 0, 1, -20874, -1160798]$ |
\(y^2+y=x^3-20874x-1160798\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 21.8.0-3.a.1.1, $\ldots$ |
$[(-2086/5, -38/5)]$ |
| 1323.h2 |
1323n3 |
1323.h |
1323n |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{9} \cdot 7^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$126$ |
$144$ |
$3$ |
$0.288584371$ |
$1$ |
|
$6$ |
$1728$ |
$0.982284$ |
$56623104/7$ |
$1.32659$ |
$5.48369$ |
$[0, 0, 1, -10584, 419060]$ |
\(y^2+y=x^3-10584x+419060\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 21.8.0-3.a.1.2, $\ldots$ |
$[(42, 220)]$ |
| 1323.h3 |
1323n1 |
1323.h |
1323n |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{3} \cdot 7^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$126$ |
$144$ |
$3$ |
$0.865753115$ |
$1$ |
|
$4$ |
$576$ |
$0.432977$ |
$884736/343$ |
$1.19875$ |
$3.98800$ |
$[0, 0, 1, -294, -1115]$ |
\(y^2+y=x^3-294x-1115\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 21.24.0-3.a.1.1, 42.48.1-42.c.1.2, 63.72.0-63.b.1.2, $\ldots$ |
$[(-7, 24)]$ |
| 1323.i1 |
1323b4 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{11} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1134$ |
$1.025103$ |
$-12288000$ |
$1.23864$ |
$5.57685$ |
$[0, 0, 1, -13230, 585758]$ |
\(y^2+y=x^3-13230x+585758\) |
|
$[]$ |
| 1323.i2 |
1323b2 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$378$ |
$0.475797$ |
$-12288000$ |
$1.23864$ |
$4.65977$ |
$[0, 0, 1, -1470, -21695]$ |
\(y^2+y=x^3-1470x-21695\) |
|
$[]$ |
| 1323.i3 |
1323b1 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$1$ |
$1$ |
|
$0$ |
$126$ |
$-0.073509$ |
$0$ |
|
$3.12007$ |
$[0, 0, 1, 0, -86]$ |
\(y^2+y=x^3-86\) |
|
$[]$ |
| 1323.i4 |
1323b3 |
1323.i |
1323b |
$4$ |
$27$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$1$ |
$1$ |
|
$0$ |
$378$ |
$0.475797$ |
$0$ |
|
$4.03716$ |
$[0, 0, 1, 0, 2315]$ |
\(y^2+y=x^3+2315\) |
|
$[]$ |
| 1323.j1 |
1323m1 |
1323.j |
1323m |
$2$ |
$3$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.044768706$ |
$1$ |
|
$2$ |
$36$ |
$-0.722146$ |
$0$ |
|
$2.03716$ |
$[0, 0, 1, 0, -2]$ |
\(y^2+y=x^3-2\) |
|
$[(2, 2)]$ |
| 1323.j2 |
1323m2 |
1323.j |
1323m |
$2$ |
$3$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.348256235$ |
$1$ |
|
$4$ |
$108$ |
$-0.172840$ |
$0$ |
|
$2.95424$ |
$[0, 0, 1, 0, 47]$ |
\(y^2+y=x^3+47\) |
|
$[(-3, 4)]$ |
| 1323.k1 |
1323a2 |
1323.k |
1323a |
$2$ |
$3$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1.602205276$ |
$1$ |
|
$2$ |
$756$ |
$0.800116$ |
$0$ |
|
$4.57861$ |
$[0, 0, 1, 0, -16207]$ |
\(y^2+y=x^3-16207\) |
|
$[(49, 318)]$ |
| 1323.k2 |
1323a1 |
1323.k |
1323a |
$2$ |
$3$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{3} \cdot 7^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$4.806615828$ |
$1$ |
|
$2$ |
$252$ |
$0.250809$ |
$0$ |
|
$3.66153$ |
$[0, 0, 1, 0, 600]$ |
\(y^2+y=x^3+600\) |
|
$[(22/3, 656/3)]$ |
| 1323.l1 |
1323c3 |
1323.l |
1323c |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{11} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$126$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$5184$ |
$1.531590$ |
$35184082944/7$ |
$1.08638$ |
$6.68424$ |
$[0, 0, 1, -187866, 31341539]$ |
\(y^2+y=x^3-187866x+31341539\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 21.8.0-3.a.1.2, $\ldots$ |
$[]$ |
| 1323.l2 |
1323c2 |
1323.l |
1323c |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{9} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$126$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$1728$ |
$0.982284$ |
$884736/343$ |
$1.19875$ |
$4.90508$ |
$[0, 0, 1, -2646, 30098]$ |
\(y^2+y=x^3-2646x+30098\) |
3.12.0.a.1, 6.24.0-3.a.1.1, 21.24.0-3.a.1.1, 42.48.1-42.c.1.2, 63.72.0-63.b.1.4, $\ldots$ |
$[]$ |
| 1323.l3 |
1323c1 |
1323.l |
1323c |
$3$ |
$9$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{3} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$126$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.432977$ |
$56623104/7$ |
$1.32659$ |
$4.56661$ |
$[0, 0, 1, -1176, -15521]$ |
\(y^2+y=x^3-1176x-15521\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 21.8.0-3.a.1.1, $\ldots$ |
$[]$ |
| 1323.m1 |
1323k1 |
1323.m |
1323k |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$-0.210294$ |
$-147$ |
$1.20397$ |
$2.89567$ |
$[1, -1, 0, -9, -36]$ |
\(y^2+xy=x^3-x^2-9x-36\) |
6.2.0.a.1 |
$[]$ |
| 1323.n1 |
1323d1 |
1323.n |
1323d |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$84$ |
$12$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$2016$ |
$0.963289$ |
$27$ |
$1.11269$ |
$4.84715$ |
$[1, -1, 0, 579, 42398]$ |
\(y^2+xy=x^3-x^2+579x+42398\) |
3.3.0.a.1, 12.6.0.h.1, 21.6.0.a.1, 84.12.1.? |
$[]$ |
| 1323.o1 |
1323o1 |
1323.o |
1323o |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{9} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$84$ |
$12$ |
$1$ |
$0.509949283$ |
$1$ |
|
$2$ |
$288$ |
$-0.009666$ |
$27$ |
$1.11269$ |
$3.22278$ |
$[1, -1, 0, 12, -127]$ |
\(y^2+xy=x^3-x^2+12x-127\) |
3.3.0.a.1, 12.6.0.h.1, 21.6.0.a.1, 84.12.1.? |
$[(16, 55)]$ |
| 1323.p1 |
1323e1 |
1323.p |
1323e |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( - 3^{5} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1260$ |
$0.762662$ |
$-147$ |
$1.20397$ |
$4.52004$ |
$[1, -1, 0, -450, 13243]$ |
\(y^2+xy=x^3-x^2-450x+13243\) |
6.2.0.a.1 |
$[]$ |
| 1323.q1 |
1323q1 |
1323.q |
1323q |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{3} \cdot 7^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$126$ |
$36$ |
$3$ |
$1.357402114$ |
$1$ |
|
$0$ |
$1344$ |
$0.556604$ |
$110592$ |
$1.11269$ |
$4.51088$ |
$[0, 0, 1, -1029, 12605]$ |
\(y^2+y=x^3-1029x+12605\) |
3.3.0.a.1, 6.6.0.c.1, 9.9.0.a.1, 18.18.1.b.1, 21.6.0.a.1, $\ldots$ |
$[(49/2, 339/2)]$ |
| 1323.r1 |
1323h1 |
1323.r |
1323h |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{11} \cdot 7^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1728$ |
$0.831999$ |
$12288/7$ |
$1.11269$ |
$4.61577$ |
$[0, 0, 1, -1323, 2315]$ |
\(y^2+y=x^3-1323x+2315\) |
42.2.0.a.1 |
$[]$ |
| 1323.s1 |
1323i1 |
1323.s |
1323i |
$1$ |
$1$ |
\( 3^{3} \cdot 7^{2} \) |
\( 3^{3} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$126$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$192$ |
$-0.416350$ |
$110592$ |
$1.11269$ |
$2.88650$ |
$[0, 0, 1, -21, -37]$ |
\(y^2+y=x^3-21x-37\) |
3.3.0.a.1, 6.6.0.c.1, 9.9.0.a.1, 18.18.1.b.1, 21.6.0.a.1, $\ldots$ |
$[]$ |
