| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$0.740617449$ |
0.193766244 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$3.703087246$ |
0.193766244 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$18.51543623$ |
0.193766244 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \cdot 17^{12} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$16.70170261$ |
$0.740617449$ |
1.618113094 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -2260076\) , \( -1308527588\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-2260076{x}-1308527588$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \cdot 17^{12} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.340340522$ |
$3.703087246$ |
1.618113094 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -2986\) , \( -114768\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-2986{x}-114768$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \cdot 17^{12} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$0.668068104$ |
$18.51543623$ |
1.618113094 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -96\) , \( 832\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-96{x}+832$ |
| 11.1-c1 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$129.0533953$ |
$0.740617449$ |
12.50309586 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-946260{x}+354609639$ |
| 11.1-c2 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{22} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$25.81067907$ |
$3.703087246$ |
12.50309586 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-1250{x}+31239$ |
| 11.1-c3 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.97614$ |
$(11,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$5.162135815$ |
$18.51543623$ |
12.50309586 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-40{x}-221$ |
| 11.1-d1 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$100$ |
\( 2 \) |
$1$ |
$0.740617449$ |
4.844156108 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -195508\) , \( -33338481\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-195508{x}-33338481$ |
| 11.1-d2 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{10} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$3.703087246$ |
4.844156108 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -258\) , \( -2981\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-258{x}-2981$ |
| 11.1-d3 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.97614$ |
$(11,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$4$ |
\( 2 \) |
$1$ |
$18.51543623$ |
4.844156108 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -8\) , \( 19\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-8{x}+19$ |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$5.54826$ |
$(17,a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$4.247877398$ |
0.277840891 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$16.99150959$ |
0.277840891 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$5.54826$ |
$(17,a+8)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$8.495754796$ |
0.277840891 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.247877398$ |
0.277840891 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{20} \) |
$5.54826$ |
$(17,a+8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.064700921$ |
$4.247877398$ |
4.517360511 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -199\) , \( -68272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-199{x}-68272$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{14} \) |
$5.54826$ |
$(17,a+8)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$16.25880368$ |
$16.99150959$ |
4.517360511 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -199\) , \( 510\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-199{x}+510$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{16} \) |
$5.54826$ |
$(17,a+8)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$16.25880368$ |
$8.495754796$ |
4.517360511 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1644\) , \( -24922\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1644{x}-24922$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{14} \) |
$5.54826$ |
$(17,a+8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$16.25880368$ |
$4.247877398$ |
4.517360511 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -26209\) , \( -1626560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-26209{x}-1626560$ |
| 17.1-c1 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 11^{12} \cdot 17^{8} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$7.904266758$ |
$4.247877398$ |
4.392257046 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -83\) , \( 18530\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-83{x}+18530$ |
| 17.1-c2 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 11^{12} \cdot 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.904266758$ |
$16.99150959$ |
4.392257046 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -83\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-83{x}-104$ |
| 17.1-c3 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 11^{12} \cdot 17^{4} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$15.80853351$ |
$8.495754796$ |
4.392257046 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -688\) , \( 7035\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-688{x}+7035$ |
| 17.1-c4 |
17.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 11^{12} \cdot 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$31.61706703$ |
$4.247877398$ |
4.392257046 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10973\) , \( 445176\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-10973{x}+445176$ |
| 17.1-d1 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 5^{12} \cdot 17^{8} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1.500953055$ |
$4.247877398$ |
7.506470431 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -17\) , \( -1734\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-17{x}-1734$ |
| 17.1-d2 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 5^{12} \cdot 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1.500953055$ |
$16.99150959$ |
7.506470431 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -17\) , \( 16\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-17{x}+16$ |
| 17.1-d3 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 5^{12} \cdot 17^{4} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$3.001906110$ |
$8.495754796$ |
7.506470431 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -142\) , \( -609\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-142{x}-609$ |
| 17.1-d4 |
17.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 5^{12} \cdot 17^{2} \) |
$5.54826$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$6.003812221$ |
$4.247877398$ |
7.506470431 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2267\) , \( -40984\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-2267{x}-40984$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 43^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 4021 a + 48030\) , \( 106753 a - 8096891\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(4021a+48030\right){x}+106753a-8096891$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 11^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 81 a - 5160\) , \( -1775 a + 141286\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(81a-5160\right){x}-1775a+141286$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{34} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -6 a - 372\) , \( 70 a + 2668\bigr] \) |
${y}^2+{y}={x}^3+\left(-6a-372\right){x}+70a+2668$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a - 120\) , \( 25 a - 41\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(a-120\right){x}+25a-41$ |
| 27.2-c1 |
27.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 89^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$9.362523918$ |
$2.993127925$ |
4.887774278 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -12267 a + 289374\) , \( 3331721 a + 56868165\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(-12267a+289374\right){x}+3331721a+56868165$ |
| 27.2-c2 |
27.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 5^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \) |
$3.120841306$ |
$2.993127925$ |
4.887774278 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 17 a - 1128\) , \( -29 a - 13986\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(17a-1128\right){x}-29a-13986$ |
| 27.2-d1 |
27.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 41^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
|
\( 2^{3} \cdot 3 \) |
$1$ |
$2.993127925$ |
6.875950944 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 133 a + 71934\) , \( -460525 a + 671778\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(133a+71934\right){x}-460525a+671778$ |
| 27.2-d2 |
27.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{22} \cdot 17^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
|
\( 2^{3} \) |
$1$ |
$2.993127925$ |
6.875950944 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 193 a - 12216\) , \( 8747 a - 513297\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(193a-12216\right){x}+8747a-513297$ |
| 27.3-a1 |
27.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 11^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -81 a - 5079\) , \( 1775 a + 139511\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-81a-5079\right){x}+1775a+139511$ |
| 27.3-a2 |
27.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 43^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -4021 a + 52051\) , \( -106753 a - 7990138\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-4021a+52051\right){x}-106753a-7990138$ |
| 27.3-b1 |
27.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -a - 119\) , \( -25 a - 16\bigr] \) |
${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-a-119\right){x}-25a-16$ |
| 27.3-b2 |
27.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{34} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.993127925$ |
0.391543000 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 a - 378\) , \( -70 a + 2738\bigr] \) |
${y}^2+{y}={x}^3+\left(6a-378\right){x}-70a+2738$ |
| 27.3-c1 |
27.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 5^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \) |
$3.120841306$ |
$2.993127925$ |
4.887774278 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -17 a - 1111\) , \( 29 a - 14015\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-17a-1111\right){x}+29a-14015$ |
| 27.3-c2 |
27.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 89^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$9.362523918$ |
$2.993127925$ |
4.887774278 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 12267 a + 277107\) , \( -3331721 a + 60199886\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(12267a+277107\right){x}-3331721a+60199886$ |
| 27.3-d1 |
27.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 17^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$4.390291062$ |
$2.993127925$ |
6.875950944 |
\( \frac{1656258560}{531441} a + \frac{649134080}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -193 a - 12023\) , \( -8747 a - 504550\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-193a-12023\right){x}-8747a-504550$ |
| 27.3-d2 |
27.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{22} \cdot 41^{12} \) |
$6.22853$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.463430354$ |
$2.993127925$ |
6.875950944 |
\( -\frac{1656258560}{531441} a + \frac{7498465280}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -133 a + 72067\) , \( 460525 a + 211253\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-133a+72067\right){x}+460525a+211253$ |
| 36.4-a1 |
36.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 41^{12} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5S4 |
$1$ |
\( 5 \) |
$3.789825710$ |
$4.298983158$ |
5.328183534 |
\( \frac{42392625}{32768} a - \frac{407435875}{32768} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -1660 a + 16965\) , \( 8428 a + 1902757\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-1660a+16965\right){x}+8428a+1902757$ |
| 36.4-a2 |
36.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 17^{12} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5S4 |
$1$ |
\( 3 \cdot 5 \) |
$1.263275236$ |
$4.298983158$ |
5.328183534 |
\( -\frac{42392625}{32768} a - \frac{182521625}{16384} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -240 a - 3600\) , \( 10080 a + 36832\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-240a-3600\right){x}+10080a+36832$ |
| 36.4-b1 |
36.4-b |
$2$ |
$23$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{6} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$23$ |
23B |
$1$ |
\( 23 \) |
$1.072002426$ |
$3.137748088$ |
5.060178864 |
\( \frac{24207807855}{8388608} a + \frac{247283058055}{4194304} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -42 a + 1266\) , \( 344 a - 7477\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-42a+1266\right){x}+344a-7477$ |
| 36.4-b2 |
36.4-b |
$2$ |
$23$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \cdot 61^{12} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$23$ |
23B |
$1$ |
\( 1 \) |
$24.65605581$ |
$3.137748088$ |
5.060178864 |
\( -\frac{24207807855}{8388608} a + \frac{518773923965}{8388608} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9626 a - 58968\) , \( -1480538 a - 4666244\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(9626a-58968\right){x}-1480538a-4666244$ |
| 36.4-c1 |
36.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5S4 |
|
\( 5 \) |
$1$ |
$4.298983158$ |
6.622445288 |
\( \frac{42392625}{32768} a - \frac{407435875}{32768} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 117\) , \( 46 a - 261\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(7a-117\right){x}+46a-261$ |
| 36.4-c2 |
36.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-935}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$6.69299$ |
$(2,a), (2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5S4 |
|
\( 3 \cdot 5 \) |
$1$ |
$4.298983158$ |
6.622445288 |
\( -\frac{42392625}{32768} a - \frac{182521625}{16384} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -a - 90\) , \( -11 a + 90\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-a-90\right){x}-11a+90$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
