| 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 |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$5.47659$ |
$(2,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$13.75037163$ |
5.147453831 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$5.47659$ |
$(2,a)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$13.75037163$ |
5.147453831 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$5.47659$ |
$(2,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$13.75037163$ |
5.147453831 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$5.47659$ |
$(2,a)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$13.75037163$ |
5.147453831 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$5.47659$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.266808954 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$5.47659$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.266808954 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$5.47659$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.266808954 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 627\) , \( -2380\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+627{x}-2380$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$5.47659$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.266808954 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 544\) , \( -2425\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+544{x}-2425$ |
| 70.2-a1 |
70.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.2 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 5 \cdot 7^{13} \) |
$6.66035$ |
$(2,a), (5,a+2), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B |
$1$ |
\( 1 \) |
$3.761654298$ |
$10.92785349$ |
3.190506991 |
\( \frac{60127}{2240} a + \frac{5094}{35} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -3 a - 75\) , \( -25 a + 415\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-3a-75\right){x}-25a+415$ |
| 70.2-a2 |
70.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.2 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2 \cdot 5^{11} \cdot 7^{23} \) |
$6.66035$ |
$(2,a), (5,a+2), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B |
$1$ |
\( 1 \) |
$41.37819727$ |
$0.993441226$ |
3.190506991 |
\( -\frac{435085890824790061}{193098314746093750} a + \frac{181874250531728909496}{96549157373046875} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -348 a + 8415\) , \( -2902 a - 53429\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-348a+8415\right){x}-2902a-53429$ |
| 70.2-b1 |
70.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.2 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 5 \cdot 7 \cdot 13^{12} \) |
$6.66035$ |
$(2,a), (5,a+2), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.3.2 |
$1$ |
\( 11 \) |
$1.181835755$ |
$10.92785349$ |
11.02632095 |
\( \frac{60127}{2240} a + \frac{5094}{35} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -9 a + 58\) , \( -92 a - 34\bigr] \) |
${y}^2+{x}{y}={x}^3+a{x}^2+\left(-9a+58\right){x}-92a-34$ |
| 70.2-b2 |
70.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.2 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2 \cdot 5^{11} \cdot 7^{11} \cdot 13^{12} \) |
$6.66035$ |
$(2,a), (5,a+2), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.3.2 |
$1$ |
\( 11 \) |
$13.00019330$ |
$0.993441226$ |
11.02632095 |
\( -\frac{435085890824790061}{193098314746093750} a + \frac{181874250531728909496}{96549157373046875} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1686 a + 24868\) , \( 36979 a - 652432\bigr] \) |
${y}^2+{x}{y}={x}^3+a{x}^2+\left(1686a+24868\right){x}+36979a-652432$ |
| 70.3-a1 |
70.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.3 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 5 \cdot 7^{13} \) |
$6.66035$ |
$(2,a), (5,a+3), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B |
$1$ |
\( 1 \) |
$3.761654298$ |
$10.92785349$ |
3.190506991 |
\( -\frac{60127}{2240} a + \frac{5094}{35} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 2 a - 75\) , \( 25 a + 415\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(2a-75\right){x}+25a+415$ |
| 70.3-a2 |
70.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.3 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2 \cdot 5^{11} \cdot 7^{23} \) |
$6.66035$ |
$(2,a), (5,a+3), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B |
$1$ |
\( 1 \) |
$41.37819727$ |
$0.993441226$ |
3.190506991 |
\( \frac{435085890824790061}{193098314746093750} a + \frac{181874250531728909496}{96549157373046875} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 347 a + 8415\) , \( 2902 a - 53429\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(347a+8415\right){x}+2902a-53429$ |
| 70.3-b1 |
70.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.3 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 5 \cdot 7 \cdot 13^{12} \) |
$6.66035$ |
$(2,a), (5,a+3), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.3.2 |
$1$ |
\( 11 \) |
$1.181835755$ |
$10.92785349$ |
11.02632095 |
\( -\frac{60127}{2240} a + \frac{5094}{35} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 9 a + 58\) , \( 92 a - 34\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(9a+58\right){x}+92a-34$ |
| 70.3-b2 |
70.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
70.3 |
\( 2 \cdot 5 \cdot 7 \) |
\( 2 \cdot 5^{11} \cdot 7^{11} \cdot 13^{12} \) |
$6.66035$ |
$(2,a), (5,a+3), (7,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.3.2 |
$1$ |
\( 11 \) |
$13.00019330$ |
$0.993441226$ |
11.02632095 |
\( \frac{435085890824790061}{193098314746093750} a + \frac{181874250531728909496}{96549157373046875} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1686 a + 24868\) , \( -36979 a - 652432\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-1686a+24868\right){x}-36979a-652432$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{4} \) |
$1$ |
$3.635347017$ |
2.158759711 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$14.54138807$ |
2.158759711 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$14.54138807$ |
2.158759711 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{4} \) |
$1$ |
$7.270694035$ |
2.158759711 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$7.270694035$ |
2.158759711 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$6.70742$ |
$(2,a), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$3.635347017$ |
2.158759711 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 72.1-b1 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
5.078837698 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 689\) , \( -2879\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+689{x}-2879$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$14.54138807$ |
5.078837698 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^3+{x}^2+3{x}+3$ |
| 72.1-b3 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$14.54138807$ |
5.078837698 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 684\) , \( -2786\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+684{x}-2786$ |
| 72.1-b4 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
5.078837698 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 679\) , \( -2721\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+679{x}-2721$ |
| 72.1-b5 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2 \) |
$1$ |
$7.270694035$ |
5.078837698 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 669\) , \( -2549\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+669{x}-2549$ |
| 72.1-b6 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$6.70742$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
5.078837698 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 589\) , \( -1803\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+589{x}-1803$ |
| 83.1-a1 |
83.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
83.1 |
\( 83 \) |
\( 83^{2} \) |
$6.95012$ |
$(83,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.177292294$ |
$13.20878018$ |
0.363520179 |
\( \frac{103823}{83} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+{x}$ |
| 83.1-b1 |
83.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
83.1 |
\( 83 \) |
\( 2^{12} \cdot 83^{2} \) |
$6.95012$ |
$(83,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$4$ |
\( 2 \) |
$1$ |
$13.20878018$ |
4.100800674 |
\( \frac{103823}{83} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 689\) , \( -2859\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+689{x}-2859$ |
| 98.2-a1 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \) |
$1$ |
$1.750834270$ |
6.062102975 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 98.2-a2 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \) |
$1$ |
$15.75750843$ |
6.062102975 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 98.2-a3 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$5.252502811$ |
6.062102975 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 98.2-a4 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.626251405$ |
6.062102975 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 98.2-a5 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2^{3} \) |
$1$ |
$7.878754216$ |
6.062102975 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 98.2-a6 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2^{3} \) |
$1$ |
$0.875417135$ |
6.062102975 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 98.2-b1 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{2} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.750834270$ |
5.503589304 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -108\) , \( -88\bigr] \) |
${y}^2+a{x}{y}={x}^3-108{x}-88$ |
| 98.2-b2 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$15.75750843$ |
5.503589304 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 572\) , \( -2616\bigr] \) |
${y}^2+a{x}{y}={x}^3+572{x}-2616$ |
| 98.2-b3 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$5.252502811$ |
5.503589304 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 592\) , \( -2944\bigr] \) |
${y}^2+a{x}{y}={x}^3+592{x}-2944$ |
| 98.2-b4 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
5.503589304 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 432\) , \( -1216\bigr] \) |
${y}^2+a{x}{y}={x}^3+432{x}-1216$ |
| 98.2-b5 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{3} \) |
$1$ |
$7.878754216$ |
5.503589304 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 532\) , \( -1960\bigr] \) |
${y}^2+a{x}{y}={x}^3+532{x}-1960$ |
| 98.2-b6 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$7.24485$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
5.503589304 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -10348\) , \( -290904\bigr] \) |
${y}^2+a{x}{y}={x}^3-10348{x}-290904$ |
| 100.2-a1 |
100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.282063771$ |
0.166176302 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 100.2-a2 |
100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$12.84619131$ |
0.166176302 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 100.2-a3 |
100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3 \) |
$1$ |
$12.84619131$ |
0.166176302 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 100.2-a4 |
100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$4.282063771$ |
0.166176302 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 100.2-b1 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$4.282063771$ |
4.486760163 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 648\) , \( -2496\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+648{x}-2496$ |
| 100.2-b2 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$12.84619131$ |
4.486760163 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 658\) , \( -2618\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+658{x}-2618$ |
| 100.2-b3 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 1 \) |
$1$ |
$12.84619131$ |
4.486760163 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 5\bigr] \) |
${y}^2={x}^3-{x}^2-5{x}+5$ |
| 100.2-b4 |
100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-166}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$7.28153$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3^{3} \) |
$1$ |
$4.282063771$ |
4.486760163 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -165\) , \( -763\bigr] \) |
${y}^2={x}^3-{x}^2-165{x}-763$ |
*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.
