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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
4488.c3 |
4488f1 |
4488.c |
4488f |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.53 |
2B |
$264$ |
$48$ |
$0$ |
$4.323630485$ |
$1$ |
|
$5$ |
$6144$ |
$0.995057$ |
$10119139303540048/85833$ |
$[0, -1, 0, -28612, 1872388]$ |
\(y^2=x^3-x^2-28612x+1872388\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 66.6.0.a.1, 132.24.0.?, $\ldots$ |
$[(-64, 1854)]$ |
8976.bd3 |
8976k1 |
8976.bd |
8976k |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.63 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$12288$ |
$0.995057$ |
$10119139303540048/85833$ |
$[0, 1, 0, -28612, -1872388]$ |
\(y^2=x^3+x^2-28612x-1872388\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 66.6.0.a.1, 132.24.0.?, $\ldots$ |
$[]$ |
13464.e3 |
13464j1 |
13464.e |
13464j |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{9} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$4.030409639$ |
$1$ |
|
$3$ |
$49152$ |
$1.544363$ |
$10119139303540048/85833$ |
$[0, 0, 0, -257511, -50296966]$ |
\(y^2=x^3-257511x-50296966\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.8, $\ldots$ |
$[(1294, 42228)]$ |
26928.t3 |
26928j1 |
26928.t |
26928j |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{9} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$98304$ |
$1.544363$ |
$10119139303540048/85833$ |
$[0, 0, 0, -257511, 50296966]$ |
\(y^2=x^3-257511x+50296966\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.6, $\ldots$ |
$[]$ |
35904.l3 |
35904bv1 |
35904.l |
35904bv |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{14} \cdot 3^{3} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.102 |
2B |
$264$ |
$48$ |
$0$ |
$9.209784082$ |
$1$ |
|
$1$ |
$98304$ |
$1.341631$ |
$10119139303540048/85833$ |
$[0, -1, 0, -114449, -14864655]$ |
\(y^2=x^3-x^2-114449x-14864655\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 66.6.0.a.1, 132.12.0.?, $\ldots$ |
$[(28729/8, 2508877/8)]$ |
35904.bx3 |
35904bn1 |
35904.bx |
35904bn |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{14} \cdot 3^{3} \cdot 11 \cdot 17^{2} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.104 |
2B |
$264$ |
$48$ |
$0$ |
$1.354423009$ |
$1$ |
|
$15$ |
$98304$ |
$1.341631$ |
$10119139303540048/85833$ |
$[0, 1, 0, -114449, 14864655]$ |
\(y^2=x^3+x^2-114449x+14864655\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 66.6.0.a.1, 132.12.0.?, $\ldots$ |
$[(259, 1632), (193, 48)]$ |
49368.o3 |
49368f1 |
49368.o |
49368f |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 11^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$737280$ |
$2.194004$ |
$10119139303540048/85833$ |
$[0, -1, 0, -3462092, -2478300108]$ |
\(y^2=x^3-x^2-3462092x-2478300108\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.1, $\ldots$ |
$[]$ |
76296.r3 |
76296v1 |
76296.r |
76296v |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 11 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$4488$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1769472$ |
$2.411663$ |
$10119139303540048/85833$ |
$[0, 1, 0, -8268964, 9149428640]$ |
\(y^2=x^3+x^2-8268964x+9149428640\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 66.6.0.a.1, 68.12.0-4.c.1.2, $\ldots$ |
$[]$ |
98736.db3 |
98736bc1 |
98736.db |
98736bc |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$1.539857765$ |
$1$ |
|
$3$ |
$1474560$ |
$2.194004$ |
$10119139303540048/85833$ |
$[0, 1, 0, -3462092, 2478300108]$ |
\(y^2=x^3+x^2-3462092x+2478300108\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.3, $\ldots$ |
$[(4021/2, 30855/2)]$ |
107712.di3 |
107712z1 |
107712.di |
107712z |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \) |
\( 2^{14} \cdot 3^{9} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$786432$ |
$1.890938$ |
$10119139303540048/85833$ |
$[0, 0, 0, -1030044, -402375728]$ |
\(y^2=x^3-1030044x-402375728\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.5, 66.6.0.a.1, $\ldots$ |
$[]$ |
107712.ej3 |
107712em1 |
107712.ej |
107712em |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 \) |
\( 2^{14} \cdot 3^{9} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$786432$ |
$1.890938$ |
$10119139303540048/85833$ |
$[0, 0, 0, -1030044, 402375728]$ |
\(y^2=x^3-1030044x+402375728\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.7, 66.6.0.a.1, $\ldots$ |
$[]$ |
112200.cq3 |
112200v1 |
112200.cq |
112200v |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$1320$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$786432$ |
$1.799776$ |
$10119139303540048/85833$ |
$[0, 1, 0, -715308, 232617888]$ |
\(y^2=x^3+x^2-715308x+232617888\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 20.12.0-4.c.1.2, 40.24.0-8.m.1.1, $\ldots$ |
$[]$ |
148104.u3 |
148104f1 |
148104.u |
148104f |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{9} \cdot 11^{7} \cdot 17^{2} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.54 |
2B |
$264$ |
$48$ |
$0$ |
$3.228917330$ |
$1$ |
|
$9$ |
$5898240$ |
$2.743309$ |
$10119139303540048/85833$ |
$[0, 0, 0, -31158831, 66945261746]$ |
\(y^2=x^3-31158831x+66945261746\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 66.6.0.a.1, 132.24.0.?, $\ldots$ |
$[(3205, 1746)]$ |
152592.g3 |
152592dc1 |
152592.g |
152592dc |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$4488$ |
$48$ |
$0$ |
$11.35856800$ |
$1$ |
|
$1$ |
$3538944$ |
$2.411663$ |
$10119139303540048/85833$ |
$[0, -1, 0, -8268964, -9149428640]$ |
\(y^2=x^3-x^2-8268964x-9149428640\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 66.6.0.a.1, 68.12.0-4.c.1.1, $\ldots$ |
$[(1350609/8, 1554170617/8)]$ |
219912.bm3 |
219912c1 |
219912.bm |
219912c |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{6} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$1848$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1769472$ |
$1.968012$ |
$10119139303540048/85833$ |
$[0, 1, 0, -1402004, -639425088]$ |
\(y^2=x^3+x^2-1402004x-639425088\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.2, 56.24.0-8.m.1.3, $\ldots$ |
$[]$ |
224400.n3 |
224400hq1 |
224400.n |
224400hq |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 11 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$1320$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$1572864$ |
$1.799776$ |
$10119139303540048/85833$ |
$[0, -1, 0, -715308, -232617888]$ |
\(y^2=x^3-x^2-715308x-232617888\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 20.12.0-4.c.1.1, 40.24.0-8.m.1.3, $\ldots$ |
$[]$ |
228888.cc3 |
228888cc1 |
228888.cc |
228888cc |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 11 \cdot 17^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$4488$ |
$48$ |
$0$ |
$1$ |
$25$ |
$5$ |
$1$ |
$14155776$ |
$2.960972$ |
$10119139303540048/85833$ |
$[0, 0, 0, -74420679, -247108993958]$ |
\(y^2=x^3-74420679x-247108993958\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 66.6.0.a.1, 132.12.0.?, $\ldots$ |
$[]$ |
296208.y3 |
296208y1 |
296208.y |
296208y |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{9} \cdot 11^{7} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.64 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$11796480$ |
$2.743309$ |
$10119139303540048/85833$ |
$[0, 0, 0, -31158831, -66945261746]$ |
\(y^2=x^3-31158831x-66945261746\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 66.6.0.a.1, 132.24.0.?, $\ldots$ |
$[]$ |
336600.eg3 |
336600eg1 |
336600.eg |
336600eg |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$1320$ |
$48$ |
$0$ |
$13.55575295$ |
$1$ |
|
$1$ |
$6291456$ |
$2.349083$ |
$10119139303540048/85833$ |
$[0, 0, 0, -6437775, -6287120750]$ |
\(y^2=x^3-6437775x-6287120750\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 60.12.0-4.c.1.2, 66.6.0.a.1, $\ldots$ |
$[(18550559/19, 79798616352/19)]$ |
394944.n3 |
394944n1 |
394944.n |
394944n |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \) |
\( 2^{14} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$3.493234622$ |
$1$ |
|
$5$ |
$11796480$ |
$2.540577$ |
$10119139303540048/85833$ |
$[0, -1, 0, -13848369, 19840249233]$ |
\(y^2=x^3-x^2-13848369x+19840249233\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.2, 66.6.0.a.1, $\ldots$ |
$[(2147, 148)]$ |
394944.ga3 |
394944ga1 |
394944.ga |
394944ga |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 \) |
\( 2^{14} \cdot 3^{3} \cdot 11^{7} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$264$ |
$48$ |
$0$ |
$6.273229506$ |
$1$ |
|
$3$ |
$11796480$ |
$2.540577$ |
$10119139303540048/85833$ |
$[0, 1, 0, -13848369, -19840249233]$ |
\(y^2=x^3+x^2-13848369x-19840249233\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.4, 66.6.0.a.1, $\ldots$ |
$[(180033, 76372296)]$ |
439824.v3 |
439824v1 |
439824.v |
439824v |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{6} \cdot 11 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$1848$ |
$48$ |
$0$ |
$4.682528827$ |
$1$ |
|
$3$ |
$3538944$ |
$1.968012$ |
$10119139303540048/85833$ |
$[0, -1, 0, -1402004, 639425088]$ |
\(y^2=x^3-x^2-1402004x+639425088\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.1, 56.24.0-8.m.1.4, $\ldots$ |
$[(784, 4640)]$ |
457776.ei3 |
457776ei1 |
457776.ei |
457776ei |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 11 \cdot 17^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$4488$ |
$48$ |
$0$ |
$4.672020959$ |
$1$ |
|
$1$ |
$28311552$ |
$2.960972$ |
$10119139303540048/85833$ |
$[0, 0, 0, -74420679, 247108993958]$ |
\(y^2=x^3-74420679x+247108993958\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 66.6.0.a.1, 132.12.0.?, $\ldots$ |
$[(50881/5, 40325904/5)]$ |