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 |
11.a1 |
11a2 |
11.a |
11a |
$3$ |
$25$ |
\( 11 \) |
\( -11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
25.120.0.3 |
5B.1.2 |
$550$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$5$ |
$0.496709$ |
$-52893159101157376/11$ |
$1.09296$ |
$16.05869$ |
$[0, -1, 1, -7820, -263580]$ |
\(y^2+y=x^3-x^2-7820x-263580\) |
5.24.0-5.a.2.2, 22.2.0.a.1, 25.120.0-25.a.2.2, 110.48.1.?, 275.600.12.?, $\ldots$ |
$[]$ |
11.a2 |
11a1 |
11.a |
11a |
$3$ |
$25$ |
\( 11 \) |
\( - 11^{5} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.120.0.1 |
5Cs.1.1 |
$550$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$4$ |
$1$ |
$-0.308010$ |
$-122023936/161051$ |
$1.01300$ |
$8.26048$ |
$[0, -1, 1, -10, -20]$ |
\(y^2+y=x^3-x^2-10x-20\) |
5.120.0-5.a.1.2, 22.2.0.a.1, 110.240.5.?, 275.600.12.?, 550.1200.37.? |
$[]$ |
11.a3 |
11a3 |
11.a |
11a |
$3$ |
$25$ |
\( 11 \) |
\( -11 \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
25.120.0.1 |
5B.1.1 |
$550$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$4$ |
$5$ |
$-1.112728$ |
$-4096/11$ |
$0.82546$ |
$4.19024$ |
$[0, -1, 1, 0, 0]$ |
\(y^2+y=x^3-x^2\) |
5.24.0-5.a.1.2, 22.2.0.a.1, 25.120.0-25.a.1.2, 110.48.1.?, 275.600.12.?, $\ldots$ |
$[]$ |
14.a1 |
14a5 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( 2^{9} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.6, 9.24.0.3 |
2B, 3B.1.2 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$0.413101$ |
$2251439055699625/25088$ |
$1.06489$ |
$13.39507$ |
$[1, 0, 1, -2731, -55146]$ |
\(y^2+xy+y=x^3-2731x-55146\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.b.1, 9.24.0-9.a.1.1, $\ldots$ |
$[]$ |
14.a2 |
14a3 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( - 2^{18} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.1, 9.24.0.3 |
2B, 3B.1.2 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$3$ |
$0.066527$ |
$-548347731625/1835008$ |
$1.02933$ |
$10.24454$ |
$[1, 0, 1, -171, -874]$ |
\(y^2+xy+y=x^3-171x-874\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.c.1, 9.24.0-9.a.1.1, $\ldots$ |
$[]$ |
14.a3 |
14a2 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( 2^{3} \cdot 7^{6} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.6, 3.24.0.1 |
2B, 3Cs.1.1 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$4$ |
$2$ |
$-0.136205$ |
$4956477625/941192$ |
$1.00821$ |
$8.45907$ |
$[1, 0, 1, -36, -70]$ |
\(y^2+xy+y=x^3-36x-70\) |
2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.b.1, 24.144.1-24.h.1.1, $\ldots$ |
$[]$ |
14.a4 |
14a6 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.6, 9.24.0.1 |
2B, 3B.1.1 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$4$ |
$6$ |
$-0.685512$ |
$128787625/98$ |
$0.96763$ |
$7.07589$ |
$[1, 0, 1, -11, 12]$ |
\(y^2+xy+y=x^3-11x+12\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.b.1, 9.24.0-9.a.1.2, $\ldots$ |
$[]$ |
14.a5 |
14a4 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.1, 9.24.0.1 |
2B, 3B.1.1 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$5$ |
$3$ |
$-1.032085$ |
$-15625/28$ |
$1.01712$ |
$4.19346$ |
$[1, 0, 1, -1, 0]$ |
\(y^2+xy+y=x^3-x\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.c.1, 9.24.0-9.a.1.2, $\ldots$ |
$[]$ |
14.a6 |
14a1 |
14.a |
14a |
$6$ |
$18$ |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.6.0.1, 3.24.0.1 |
2B, 3Cs.1.1 |
$504$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$5$ |
$1$ |
$-0.482779$ |
$9938375/21952$ |
$0.98695$ |
$6.49759$ |
$[1, 0, 1, 4, -6]$ |
\(y^2+xy+y=x^3+4x-6\) |
2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$ |
$[]$ |
15.a1 |
15a5 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.148 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$1114544804970241/405$ |
$1.07354$ |
$12.79416$ |
$[1, 1, 1, -2160, -39540]$ |
\(y^2+xy+y=x^3+x^2-2160x-39540\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 10.6.0.a.1, 16.96.0-16.x.2.4, $\ldots$ |
$[]$ |
15.a2 |
15a2 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.58 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.055704$ |
$272223782641/164025$ |
$1.03897$ |
$9.72282$ |
$[1, 1, 1, -135, -660]$ |
\(y^2+xy+y=x^3+x^2-135x-660\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.k.1.1, 20.48.0-20.c.1.2, 40.192.1-40.cc.2.4, $\ldots$ |
$[]$ |
15.a3 |
15a6 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3^{16} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.153 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$-147281603041/215233605$ |
$1.05949$ |
$9.96125$ |
$[1, 1, 1, -110, -880]$ |
\(y^2+xy+y=x^3+x^2-110x-880\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 16.96.0-16.u.2.3, 20.24.0-20.h.1.1, $\ldots$ |
$[]$ |
15.a4 |
15a7 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.5 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.402277$ |
$56667352321/15$ |
$1.03019$ |
$9.14328$ |
$[1, 1, 1, -80, 242]$ |
\(y^2+xy+y=x^3+x^2-80x+242\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.by.2.3, $\ldots$ |
$[]$ |
15.a5 |
15a1 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.3 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.402277$ |
$111284641/50625$ |
$1.02534$ |
$6.84168$ |
$[1, 1, 1, -10, -10]$ |
\(y^2+xy+y=x^3+x^2-10x-10\) |
2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.9, 24.192.1-24.n.1.1, 40.192.1-40.s.1.5, $\ldots$ |
$[]$ |
15.a6 |
15a3 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.7 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.748851$ |
$13997521/225$ |
$0.96230$ |
$6.07610$ |
$[1, 1, 1, -5, 2]$ |
\(y^2+xy+y=x^3+x^2-5x+2\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.i.1.10, 16.96.0-16.d.2.3, 24.96.0-24.bb.2.5, $\ldots$ |
$[]$ |
15.a7 |
15a8 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.5 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-1.095425$ |
$-1/15$ |
$1.19808$ |
$3.75281$ |
$[1, 1, 1, 0, 0]$ |
\(y^2+xy+y=x^3+x^2\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.bz.1.3, $\ldots$ |
$[]$ |
15.a8 |
15a4 |
15.a |
15a |
$8$ |
$16$ |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{8} \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.96.0.99 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.055704$ |
$4733169839/3515625$ |
$1.05585$ |
$8.22653$ |
$[1, 1, 1, 35, -28]$ |
\(y^2+xy+y=x^3+x^2+35x-28\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.5, 24.192.1-24.cv.2.2, 80.192.1.?, $\ldots$ |
$[]$ |
17.a1 |
17a3 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.18 |
2B |
$1088$ |
$1536$ |
$53$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$-0.376636$ |
$82483294977/17$ |
$1.03131$ |
$8.87186$ |
$[1, -1, 1, -91, -310]$ |
\(y^2+xy+y=x^3-x^2-91x-310\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 16.48.0-16.j.1.3, 32.96.0-32.f.2.1, $\ldots$ |
$[]$ |
17.a2 |
17a2 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( 17^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.13 |
2Cs |
$544$ |
$1536$ |
$53$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.723209$ |
$20346417/289$ |
$1.02963$ |
$5.93969$ |
$[1, -1, 1, -6, -4]$ |
\(y^2+xy+y=x^3-x^2-6x-4\) |
2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.f.1.1, 16.96.0-16.c.2.2, 68.48.0-68.b.1.1, $\ldots$ |
$[]$ |
17.a3 |
17a1 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( - 17^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.96.0.32 |
2B |
$1088$ |
$1536$ |
$53$ |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.376636$ |
$-35937/83521$ |
$1.18071$ |
$6.63128$ |
$[1, -1, 1, -1, -14]$ |
\(y^2+xy+y=x^3-x^2-x-14\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.t.1.2, 16.96.0-16.m.2.1, 136.96.1.?, $\ldots$ |
$[]$ |
17.a4 |
17a4 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( 17 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.10 |
2B |
$1088$ |
$1536$ |
$53$ |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-1.069784$ |
$35937/17$ |
$1.02432$ |
$3.70234$ |
$[1, -1, 1, -1, 0]$ |
\(y^2+xy+y=x^3-x^2-x\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 16.48.0-16.j.1.1, 32.96.0-32.f.2.2, $\ldots$ |
$[]$ |
19.a1 |
19a2 |
19.a |
19a |
$3$ |
$9$ |
\( 19 \) |
\( -19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.2 |
3B.1.2 |
$1026$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$0$ |
$3$ |
$0.033439$ |
$-50357871050752/19$ |
$1.10495$ |
$10.71517$ |
$[0, 1, 1, -769, -8470]$ |
\(y^2+y=x^3+x^2-769x-8470\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
$[]$ |
19.a2 |
19a1 |
19.a |
19a |
$3$ |
$9$ |
\( 19 \) |
\( - 19^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$1026$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.515867$ |
$-89915392/6859$ |
$1.03310$ |
$6.26204$ |
$[0, 1, 1, -9, -15]$ |
\(y^2+y=x^3+x^2-9x-15\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$ |
$[]$ |
19.a3 |
19a3 |
19.a |
19a |
$3$ |
$9$ |
\( 19 \) |
\( -19 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.1 |
3B.1.1 |
$1026$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.065172$ |
$32768/19$ |
$1.31757$ |
$3.53113$ |
$[0, 1, 1, 1, 0]$ |
\(y^2+y=x^3+x^2+x\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
$[]$ |
20.a1 |
20a4 |
20.a |
20a |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.22, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$6$ |
$-0.380644$ |
$488095744/125$ |
$1.07376$ |
$7.60369$ |
$[0, 1, 0, -41, -116]$ |
\(y^2=x^3+x^2-41x-116\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.2, $\ldots$ |
$[]$ |
20.a2 |
20a3 |
20.a |
20a |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.37, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$3$ |
$-0.034070$ |
$-20720464/15625$ |
$0.95894$ |
$7.75305$ |
$[0, 1, 0, -36, -140]$ |
\(y^2=x^3+x^2-36x-140\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.a.1, 6.24.0-6.a.1.2, 8.12.0-4.a.1.1, $\ldots$ |
$[]$ |
20.a3 |
20a2 |
20.a |
20a |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.22, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$5$ |
$2$ |
$-0.929950$ |
$16384/5$ |
$0.95621$ |
$4.16481$ |
$[0, 1, 0, -1, 0]$ |
\(y^2=x^3+x^2-x\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.2, $\ldots$ |
$[]$ |
20.a4 |
20a1 |
20.a |
20a |
$4$ |
$6$ |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.37, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$5$ |
$1$ |
$-0.583377$ |
$21296/25$ |
$0.83964$ |
$5.18725$ |
$[0, 1, 0, 4, 4]$ |
\(y^2=x^3+x^2+4x+4\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.a.1, 6.24.0-6.a.1.4, 8.12.0-4.a.1.1, $\ldots$ |
$[]$ |
21.a1 |
21a5 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$53297461115137/147$ |
$1.05087$ |
$10.38157$ |
$[1, 0, 0, -784, -8515]$ |
\(y^2+xy=x^3-784x-8515\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 16.48.0-16.e.2.5, $\ldots$ |
$[]$ |
21.a2 |
21a2 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.34 |
2Cs |
$168$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.272368$ |
$13027640977/21609$ |
$1.08149$ |
$7.64992$ |
$[1, 0, 0, -49, -136]$ |
\(y^2+xy=x^3-49x-136\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 12.48.0-12.c.1.3, 24.96.0-24.j.2.5, $\ldots$ |
$[]$ |
21.a3 |
21a3 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7 \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.159 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.272368$ |
$6570725617/45927$ |
$1.00160$ |
$7.42510$ |
$[1, 0, 0, -39, 90]$ |
\(y^2+xy=x^3-39x+90\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 28.24.0-28.h.1.2, 48.96.0-48.bf.1.3, $\ldots$ |
$[]$ |
21.a4 |
21a6 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( - 3 \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.177 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$-4354703137/17294403$ |
$1.04266$ |
$7.96731$ |
$[1, 0, 0, -34, -217]$ |
\(y^2+xy=x^3-34x-217\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.bb.2.3, 12.24.0-12.g.1.1, $\ldots$ |
$[]$ |
21.a5 |
21a1 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.24 |
2Cs |
$168$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.618942$ |
$7189057/3969$ |
$1.14862$ |
$5.18573$ |
$[1, 0, 0, -4, -1]$ |
\(y^2+xy=x^3-4x-1\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.w.2.6, 28.48.0-28.c.1.1, $\ldots$ |
$[]$ |
21.a6 |
21a4 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.27 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.965515$ |
$103823/63$ |
$0.97868$ |
$3.79384$ |
$[1, 0, 0, 1, 0]$ |
\(y^2+xy=x^3+x\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 14.6.0.b.1, 16.48.0-16.e.1.2, $\ldots$ |
$[]$ |
24.a1 |
24a5 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.135 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$0.047795$ |
$3065617154/9$ |
$1.21059$ |
$9.27238$ |
$[0, -1, 0, -384, -2772]$ |
\(y^2=x^3-x^2-384x-2772\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 16.96.0-16.l.1.6, 24.96.0-24.bf.1.4, $\ldots$ |
$[]$ |
24.a2 |
24a3 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.106 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.298779$ |
$28756228/3$ |
$1.05617$ |
$7.58509$ |
$[0, -1, 0, -64, 220]$ |
\(y^2=x^3-x^2-64x+220\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 12.24.0-12.h.1.2, 16.96.0-16.bb.2.4, $\ldots$ |
$[]$ |
24.a3 |
24a2 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.49 |
2Cs |
$24$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.298779$ |
$1556068/81$ |
$1.03212$ |
$6.66733$ |
$[0, -1, 0, -24, -36]$ |
\(y^2=x^3-x^2-24x-36\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.e.2.2, 24.192.1-24.bl.2.4 |
$[]$ |
24.a4 |
24a1 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.42 |
2Cs |
$24$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$7$ |
$1$ |
$-0.645352$ |
$35152/9$ |
$0.97255$ |
$5.03850$ |
$[0, -1, 0, -4, 4]$ |
\(y^2=x^3-x^2-4x+4\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.h.1.6, 12.48.0-12.c.1.1, 24.192.1-24.bu.1.7 |
$[]$ |
24.a5 |
24a4 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.110 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.991926$ |
$2048/3$ |
$1.17572$ |
$3.40564$ |
$[0, -1, 0, 1, 0]$ |
\(y^2=x^3-x^2+x\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 8.48.0-8.ba.1.2, 12.24.0-12.g.1.2, $\ldots$ |
$[]$ |
24.a6 |
24a6 |
24.a |
24a |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \) |
\( - 2^{11} \cdot 3^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.166 |
2B |
$48$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$4$ |
$0.047795$ |
$207646/6561$ |
$1.15980$ |
$7.50451$ |
$[0, -1, 0, 16, -180]$ |
\(y^2=x^3-x^2+16x-180\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.96.0-8.m.1.2, 48.192.1-48.w.2.4 |
$[]$ |
26.a1 |
26a2 |
26.a |
26a |
$3$ |
$9$ |
\( 2 \cdot 13 \) |
\( - 2^{9} \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.3 |
3B.1.2 |
$936$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$0.054386$ |
$-10730978619193/6656$ |
$1.02193$ |
$9.20911$ |
$[1, 0, 1, -460, -3830]$ |
\(y^2+xy+y=x^3-460x-3830\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$ |
$[]$ |
26.a2 |
26a1 |
26.a |
26a |
$3$ |
$9$ |
\( 2 \cdot 13 \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$936$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.494920$ |
$-10218313/17576$ |
$0.94717$ |
$5.37707$ |
$[1, 0, 1, -5, -8]$ |
\(y^2+xy+y=x^3-5x-8\) |
3.24.0-3.a.1.1, 104.2.0.?, 117.72.0.?, 312.48.1.?, 936.144.3.? |
$[]$ |
26.a3 |
26a3 |
26.a |
26a |
$3$ |
$9$ |
\( 2 \cdot 13 \) |
\( - 2 \cdot 13 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$936$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-1.044226$ |
$12167/26$ |
$0.84415$ |
$3.19113$ |
$[1, 0, 1, 0, 0]$ |
\(y^2+xy+y=x^3\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$ |
$[]$ |
26.b1 |
26b2 |
26.b |
26b |
$2$ |
$7$ |
\( 2 \cdot 13 \) |
\( - 2 \cdot 13^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.5 |
7B.1.3 |
$728$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$14$ |
$0.289794$ |
$-1064019559329/125497034$ |
$1.06269$ |
$8.55670$ |
$[1, -1, 1, -213, -1257]$ |
\(y^2+xy+y=x^3-x^2-213x-1257\) |
7.48.0-7.a.2.2, 104.2.0.?, 728.96.2.? |
$[]$ |
26.b2 |
26b1 |
26.b |
26b |
$2$ |
$7$ |
\( 2 \cdot 13 \) |
\( - 2^{7} \cdot 13 \) |
$0$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$728$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.683161$ |
$-2146689/1664$ |
$0.96784$ |
$4.73570$ |
$[1, -1, 1, -3, 3]$ |
\(y^2+xy+y=x^3-x^2-3x+3\) |
7.48.0-7.a.1.2, 104.2.0.?, 728.96.2.? |
$[]$ |
27.a1 |
27a2 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.13.34 |
3B.1.2 |
|
|
|
$1$ |
$1$ |
|
$0$ |
$3$ |
$0.052148$ |
$-12288000$ |
$1.23864$ |
$8.61966$ |
$[0, 0, 1, -270, -1708]$ |
\(y^2+y=x^3-270x-1708\) |
|
$[]$ |
27.a2 |
27a4 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{5} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.13.25 |
3B.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$9$ |
$-0.497158$ |
$-12288000$ |
$1.23864$ |
$6.61966$ |
$[0, 0, 1, -30, 63]$ |
\(y^2+y=x^3-30x+63\) |
|
$[]$ |
27.a3 |
27a1 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{9} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.1944.55.37 |
3Cs.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.497158$ |
$0$ |
|
$5.26186$ |
$[0, 0, 1, 0, -7]$ |
\(y^2+y=x^3-7\) |
|
$[]$ |
27.a4 |
27a3 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.1944.55.31 |
3Cs.1.1 |
|
|
|
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.046465$ |
$0$ |
|
$3.26186$ |
$[0, 0, 1, 0, 0]$ |
\(y^2+y=x^3\) |
|
$[]$ |
30.a1 |
30a7 |
30.a |
30a |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{3} \cdot 3^{4} \cdot 5^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.7, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$24$ |
$0.564166$ |
$16778985534208729/81000$ |
$1.08181$ |
$10.98404$ |
$[1, 0, 1, -5334, -150368]$ |
\(y^2+xy+y=x^3-5334x-150368\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.3, $\ldots$ |
$[]$ |