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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
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 |
$1$ |
$1$ |
|
$0$ |
$5$ |
$0.496709$ |
$-52893159101157376/11$ |
$[0, -1, 1, -7820, -263580]$ |
\(y^2+y=x^3-x^2-7820x-263580\) |
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 |
$1$ |
$1$ |
|
$4$ |
$1$ |
$-0.308010$ |
$-122023936/161051$ |
$[0, -1, 1, -10, -20]$ |
\(y^2+y=x^3-x^2-10x-20\) |
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 |
$1$ |
$1$ |
|
$4$ |
$5$ |
$-1.112728$ |
$-4096/11$ |
$[0, -1, 1, 0, 0]$ |
\(y^2+y=x^3-x^2\) |
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 |
$1$ |
$1$ |
|
$0$ |
$6$ |
$0.413101$ |
$2251439055699625/25088$ |
$[1, 0, 1, -2731, -55146]$ |
\(y^2+xy+y=x^3-2731x-55146\) |
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 |
$1$ |
$1$ |
|
$1$ |
$3$ |
$0.066527$ |
$-548347731625/1835008$ |
$[1, 0, 1, -171, -874]$ |
\(y^2+xy+y=x^3-171x-874\) |
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 |
$1$ |
$1$ |
|
$4$ |
$2$ |
$-0.136205$ |
$4956477625/941192$ |
$[1, 0, 1, -36, -70]$ |
\(y^2+xy+y=x^3-36x-70\) |
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 |
$1$ |
$1$ |
|
$4$ |
$6$ |
$-0.685512$ |
$128787625/98$ |
$[1, 0, 1, -11, 12]$ |
\(y^2+xy+y=x^3-11x+12\) |
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 |
$1$ |
$1$ |
|
$5$ |
$3$ |
$-1.032085$ |
$-15625/28$ |
$[1, 0, 1, -1, 0]$ |
\(y^2+xy+y=x^3-x\) |
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 |
$1$ |
$1$ |
|
$5$ |
$1$ |
$-0.482779$ |
$9938375/21952$ |
$[1, 0, 1, 4, -6]$ |
\(y^2+xy+y=x^3+4x-6\) |
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 |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$1114544804970241/405$ |
$[1, 1, 1, -2160, -39540]$ |
\(y^2+xy+y=x^3+x^2-2160x-39540\) |
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 |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.055704$ |
$272223782641/164025$ |
$[1, 1, 1, -135, -660]$ |
\(y^2+xy+y=x^3+x^2-135x-660\) |
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 |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.290870$ |
$-147281603041/215233605$ |
$[1, 1, 1, -110, -880]$ |
\(y^2+xy+y=x^3+x^2-110x-880\) |
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 |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.402277$ |
$56667352321/15$ |
$[1, 1, 1, -80, 242]$ |
\(y^2+xy+y=x^3+x^2-80x+242\) |
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 |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.402277$ |
$111284641/50625$ |
$[1, 1, 1, -10, -10]$ |
\(y^2+xy+y=x^3+x^2-10x-10\) |
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 |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.748851$ |
$13997521/225$ |
$[1, 1, 1, -5, 2]$ |
\(y^2+xy+y=x^3+x^2-5x+2\) |
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 |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-1.095425$ |
$-1/15$ |
$[1, 1, 1, 0, 0]$ |
\(y^2+xy+y=x^3+x^2\) |
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 |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.055704$ |
$4733169839/3515625$ |
$[1, 1, 1, 35, -28]$ |
\(y^2+xy+y=x^3+x^2+35x-28\) |
17.a1 |
17a3 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.18 |
2B |
$1$ |
$1$ |
|
$0$ |
$4$ |
$-0.376636$ |
$82483294977/17$ |
$[1, -1, 1, -91, -310]$ |
\(y^2+xy+y=x^3-x^2-91x-310\) |
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 |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.723209$ |
$20346417/289$ |
$[1, -1, 1, -6, -4]$ |
\(y^2+xy+y=x^3-x^2-6x-4\) |
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 |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.376636$ |
$-35937/83521$ |
$[1, -1, 1, -1, -14]$ |
\(y^2+xy+y=x^3-x^2-x-14\) |
17.a4 |
17a4 |
17.a |
17a |
$4$ |
$4$ |
\( 17 \) |
\( 17 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
32.96.0.10 |
2B |
$1$ |
$1$ |
|
$3$ |
$4$ |
$-1.069784$ |
$35937/17$ |
$[1, -1, 1, -1, 0]$ |
\(y^2+xy+y=x^3-x^2-x\) |
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 |
$1$ |
$1$ |
|
$0$ |
$3$ |
$0.033439$ |
$-50357871050752/19$ |
$[0, 1, 1, -769, -8470]$ |
\(y^2+y=x^3+x^2-769x-8470\) |
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 |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.515867$ |
$-89915392/6859$ |
$[0, 1, 1, -9, -15]$ |
\(y^2+y=x^3+x^2-9x-15\) |
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 |
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.065172$ |
$32768/19$ |
$[0, 1, 1, 1, 0]$ |
\(y^2+y=x^3+x^2+x\) |
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 |
$1$ |
$1$ |
|
$1$ |
$6$ |
$-0.380644$ |
$488095744/125$ |
$[0, 1, 0, -41, -116]$ |
\(y^2=x^3+x^2-41x-116\) |
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 |
$1$ |
$1$ |
|
$1$ |
$3$ |
$-0.034070$ |
$-20720464/15625$ |
$[0, 1, 0, -36, -140]$ |
\(y^2=x^3+x^2-36x-140\) |
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 |
$1$ |
$1$ |
|
$5$ |
$2$ |
$-0.929950$ |
$16384/5$ |
$[0, 1, 0, -1, 0]$ |
\(y^2=x^3+x^2-x\) |
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 |
$1$ |
$1$ |
|
$5$ |
$1$ |
$-0.583377$ |
$21296/25$ |
$[0, 1, 0, 4, 4]$ |
\(y^2=x^3+x^2+4x+4\) |
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 |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$53297461115137/147$ |
$[1, 0, 0, -784, -8515]$ |
\(y^2+xy=x^3-784x-8515\) |
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 |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.272368$ |
$13027640977/21609$ |
$[1, 0, 0, -49, -136]$ |
\(y^2+xy=x^3-49x-136\) |
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 |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.272368$ |
$6570725617/45927$ |
$[1, 0, 0, -39, 90]$ |
\(y^2+xy=x^3-39x+90\) |
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 |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$-4354703137/17294403$ |
$[1, 0, 0, -34, -217]$ |
\(y^2+xy=x^3-34x-217\) |
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 |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.618942$ |
$7189057/3969$ |
$[1, 0, 0, -4, -1]$ |
\(y^2+xy=x^3-4x-1\) |
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 |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.965515$ |
$103823/63$ |
$[1, 0, 0, 1, 0]$ |
\(y^2+xy=x^3+x\) |
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 |
$1$ |
$1$ |
|
$1$ |
$4$ |
$0.047795$ |
$3065617154/9$ |
$[0, -1, 0, -384, -2772]$ |
\(y^2=x^3-x^2-384x-2772\) |
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 |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.298779$ |
$28756228/3$ |
$[0, -1, 0, -64, 220]$ |
\(y^2=x^3-x^2-64x+220\) |
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 |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.298779$ |
$1556068/81$ |
$[0, -1, 0, -24, -36]$ |
\(y^2=x^3-x^2-24x-36\) |
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 |
$1$ |
$1$ |
|
$7$ |
$1$ |
$-0.645352$ |
$35152/9$ |
$[0, -1, 0, -4, 4]$ |
\(y^2=x^3-x^2-4x+4\) |
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 |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.991926$ |
$2048/3$ |
$[0, -1, 0, 1, 0]$ |
\(y^2=x^3-x^2+x\) |
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 |
$1$ |
$1$ |
|
$1$ |
$4$ |
$0.047795$ |
$207646/6561$ |
$[0, -1, 0, 16, -180]$ |
\(y^2=x^3-x^2+16x-180\) |
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 |
$1$ |
$1$ |
|
$0$ |
$6$ |
$0.054386$ |
$-10730978619193/6656$ |
$[1, 0, 1, -460, -3830]$ |
\(y^2+xy+y=x^3-460x-3830\) |
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 |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.494920$ |
$-10218313/17576$ |
$[1, 0, 1, -5, -8]$ |
\(y^2+xy+y=x^3-5x-8\) |
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 |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-1.044226$ |
$12167/26$ |
$[1, 0, 1, 0, 0]$ |
\(y^2+xy+y=x^3\) |
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 |
$1$ |
$1$ |
|
$0$ |
$14$ |
$0.289794$ |
$-1064019559329/125497034$ |
$[1, -1, 1, -213, -1257]$ |
\(y^2+xy+y=x^3-x^2-213x-1257\) |
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 |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.683161$ |
$-2146689/1664$ |
$[1, -1, 1, -3, 3]$ |
\(y^2+xy+y=x^3-x^2-3x+3\) |
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 |
$1$ |
$1$ |
|
$0$ |
$3$ |
$0.052148$ |
$-12288000$ |
$[0, 0, 1, -270, -1708]$ |
\(y^2+y=x^3-270x-1708\) |
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 |
$1$ |
$1$ |
|
$2$ |
$9$ |
$-0.497158$ |
$-12288000$ |
$[0, 0, 1, -30, 63]$ |
\(y^2+y=x^3-30x+63\) |
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 |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.497158$ |
$0$ |
$[0, 0, 1, 0, -7]$ |
\(y^2+y=x^3-7\) |
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 |
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.046465$ |
$0$ |
$[0, 0, 1, 0, 0]$ |
\(y^2+y=x^3\) |
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 |
$1$ |
$1$ |
|
$0$ |
$24$ |
$0.564166$ |
$16778985534208729/81000$ |
$[1, 0, 1, -5334, -150368]$ |
\(y^2+xy+y=x^3-5334x-150368\) |