| 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 |
| 147.2-a5 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.448307718$ |
0.497720347 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 14700.2-g4 |
14700.2-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14700.2 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$1.70423$ |
$(-2a+1), (-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.221038741$ |
2.041868430 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1070{x}+7812$ |
| 59241.5-b5 |
59241.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
59241.5 |
\( 3 \cdot 7^{2} \cdot 13 \cdot 31 \) |
\( 3^{8} \cdot 7^{10} \cdot 13^{4} \cdot 31^{2} \) |
$2.41465$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (-6a+1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.301724512$ |
1.393605825 |
\( \frac{20398821354259170080}{12816402437621601} a + \frac{11153797193332261787}{4272134145873867} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 80 a - 655\) , \( -240 a + 4296\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(80a-655\right){x}-240a+4296$ |
| 59241.8-b5 |
59241.8-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
59241.8 |
\( 3 \cdot 7^{2} \cdot 13 \cdot 31 \) |
\( 3^{8} \cdot 7^{10} \cdot 13^{4} \cdot 31^{2} \) |
$2.41465$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (6a-5)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.301724512$ |
1.393605825 |
\( -\frac{20398821354259170080}{12816402437621601} a + \frac{53860212934255955441}{12816402437621601} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 655 a - 79\) , \( -336 a + 4711\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(655a-79\right){x}-336a+4711$ |
| 225.2-a5 |
225.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$0.69217$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.117850856$ |
0.558925428 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 36\) , \( 28\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+36{x}+28$ |
| 7650.3-d7 |
7650.3-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7650.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{12} \cdot 17^{2} \) |
$1.67141$ |
$(a+1), (-a-2), (2a+1), (a+4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.740294391$ |
2.961177564 |
\( -\frac{258586287011}{1016015625} a - \frac{5113528783469}{5418750000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 25 i - 65\) , \( 222 i - 304\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(25i-65\right){x}+222i-304$ |
| 7650.4-d7 |
7650.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7650.4 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{12} \cdot 17^{2} \) |
$1.67141$ |
$(a+1), (-a-2), (2a+1), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.740294391$ |
2.961177564 |
\( \frac{258586287011}{1016015625} a - \frac{5113528783469}{5418750000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -25 i - 65\) , \( -222 i - 304\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-25i-65\right){x}-222i-304$ |
| 22050.2-d4 |
22050.2-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$2.17781$ |
$(a+1), (-a-2), (2a+1), (3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{12} \) |
$1$ |
$0.221038741$ |
3.536619863 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -1070\) , \( -7812\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-1070{x}-7812$ |
| 252.2-a3 |
252.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$0.94197$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$2.740367332$ |
2.071522989 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
| 6300.2-c5 |
6300.2-c |
$10$ |
$32$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6300.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{32} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \) |
$2.10631$ |
$(a), (-a+1), (-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{12} \) |
$0.621045073$ |
$0.442077482$ |
6.641290386 |
\( \frac{1023887723039}{928972800} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 900\bigr] \) |
${y}^2+{x}{y}={x}^{3}+210{x}+900$ |
| 6300.2-c6 |
6300.2-c |
$10$ |
$32$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6300.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$2.10631$ |
$(a), (-a+1), (-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{12} \) |
$1.242090147$ |
$0.221038741$ |
6.641290386 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1070{x}+7812$ |
| 144.2-a1 |
144.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.87554$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$1.817673508$ |
1.285289264 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 5\) , \( -22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+5{x}-22$ |
| 5202.5-i5 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.735016588$ |
4.157881714 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-114{x}-396$ |
| 22050.2-d4 |
22050.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$3.07989$ |
$(a), (-a-1), (a-1), (5), (7)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{13} \) |
$1$ |
$0.221038741$ |
5.001535775 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1070{x}+7812$ |
| 44100.5-r4 |
44100.5-r |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
44100.5 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$4.29482$ |
$(-a), (a-1), (-a-1), (a-2), (2), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{14} \) |
$0.650582857$ |
$0.221038741$ |
11.09978681 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1070{x}+7812$ |
| 45.1-a5 |
45.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$0.51752$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$7.846755528$ |
0.438646969 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 45.1-a6 |
45.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$0.51752$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$31.38702211$ |
0.438646969 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 882.1-a6 |
882.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
882.1 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$1.37737$ |
$(a), (-2a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$12.07873502$ |
2.135238861 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 24.1-b5 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$22.73403407$ |
0.820343793 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 23 a - 44\) , \( -68 a + 116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(23a-44\right){x}-68a+116$ |
| 1794.1-s4 |
1794.1-s |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1794.1 |
\( 2 \cdot 3 \cdot 13 \cdot 23 \) |
\( 2^{8} \cdot 3^{8} \cdot 13^{4} \cdot 23^{2} \) |
$2.01458$ |
$(a+1), (a), (a-4), (-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.919584078$ |
$4.866358860$ |
5.167315077 |
\( -\frac{1755833455621465}{2447620578} a + \frac{24363423214296289}{19580964624} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -47 a - 164\) , \( -129 a + 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-47a-164\right){x}-129a+26$ |
| 1794.4-s6 |
1794.4-s |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1794.4 |
\( 2 \cdot 3 \cdot 13 \cdot 23 \) |
\( 2^{8} \cdot 3^{8} \cdot 13^{4} \cdot 23^{2} \) |
$2.01458$ |
$(a+1), (a), (a+4), (3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.919584078$ |
$4.866358860$ |
5.167315077 |
\( \frac{1755833455621465}{2447620578} a + \frac{24363423214296289}{19580964624} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 46 a - 164\) , \( 129 a + 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(46a-164\right){x}+129a+26$ |
| 468.1-f4 |
468.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{24} \cdot 3^{4} \cdot 13^{4} \) |
$1.71366$ |
$(-a+2), (-a-1), (-2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$4.274544063$ |
4.146916864 |
\( -\frac{483282106779025}{16845963264} a + \frac{1291964330133317}{16845963264} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -620 a - 971\) , \( -8796 a - 13731\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-620a-971\right){x}-8796a-13731$ |
| 468.2-f5 |
468.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
468.2 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{24} \cdot 3^{4} \cdot 13^{4} \) |
$1.71366$ |
$(-a+2), (-a-1), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$4.274544063$ |
4.146916864 |
\( \frac{483282106779025}{16845963264} a + \frac{202170555838573}{4211490816} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 619 a - 1591\) , \( 8795 a - 22527\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(619a-1591\right){x}+8795a-22527$ |
| 612.1-e5 |
612.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
612.1 |
\( 2^{2} \cdot 3^{2} \cdot 17 \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.83253$ |
$(-a+2), (-a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$8.757787080$ |
4.248150726 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 2100.1-v4 |
2100.1-v |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
2100.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \) |
$2.77206$ |
$(-a+2), (-a), (-a+1), (a+3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{12} \) |
$1$ |
$1.052538541$ |
3.674923837 |
\( \frac{135487869158881}{51438240000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1070{x}+7812$ |
| 63.1-a5 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$1.33215$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$13.02432697$ |
1.230683220 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 126.1-a4 |
126.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$1.58420$ |
$(a+3), (-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$2.486887276$ |
3.759820155 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -103\) , \( -205\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-103{x}-205$ |
| 595.1-A2 |
595.1-A |
$10$ |
$32$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
595.1 |
\( 5 \cdot 7 \cdot 17 \) |
\( 5^{4} \cdot 7^{2} \cdot 17^{2} \) |
$1.24286$ |
$(a^2+1), (2a^2-a), (-a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$28.77896236$ |
0.750103559 |
\( \frac{16132001251033}{8850625} a^{2} - \frac{28240457747472}{8850625} a + \frac{21323168341476}{8850625} \) |
\( \bigl[a^{2} + 1\) , \( -a^{2} - a + 1\) , \( a\) , \( -5 a^{2} + 9 a - 5\) , \( 5 a^{2} - 9 a + 6\bigr] \) |
${y}^2+\left(a^{2}+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-5a^{2}+9a-5\right){x}+5a^{2}-9a+6$ |
| 595.1-A4 |
595.1-A |
$10$ |
$32$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
595.1 |
\( 5 \cdot 7 \cdot 17 \) |
\( 5^{8} \cdot 7^{4} \cdot 17^{4} \) |
$1.24286$ |
$(a^2+1), (2a^2-a), (-a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$7.194740591$ |
0.750103559 |
\( -\frac{324960118969716738}{78333562890625} a^{2} - \frac{155368957384973183}{78333562890625} a + \frac{322393888249260514}{78333562890625} \) |
\( \bigl[a^{2} + 1\) , \( -a^{2} - a + 1\) , \( a\) , \( -10 a^{2} + 14 a\) , \( -7 a^{2} - 11 a + 5\bigr] \) |
${y}^2+\left(a^{2}+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-10a^{2}+14a\right){x}-7a^{2}-11a+5$ |
| 805.2-A2 |
805.2-A |
$8$ |
$16$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
805.2 |
\( 5 \cdot 7 \cdot 23 \) |
\( 5^{4} \cdot 7^{8} \cdot 23^{2} \) |
$1.30708$ |
$(a^2+1), (2a^2-a), (-a^2-2a+2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.153083236$ |
0.850017686 |
\( \frac{3687966726825902}{1905987330625} a^{2} - \frac{6470140329660943}{1905987330625} a + \frac{4903395776718594}{1905987330625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -5 a^{2} + 8 a - 5\) , \( -4 a^{2} + 9 a - 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5a^{2}+8a-5\right){x}-4a^{2}+9a-4$ |
| 875.1-A2 |
875.1-A |
$8$ |
$16$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
875.1 |
\( 5^{3} \cdot 7 \) |
\( 5^{12} \cdot 7^{2} \) |
$1.32537$ |
$(a^2+1), (2a^2-a), (a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$16.02371778$ |
0.835294031 |
\( \frac{171107912793}{19140625} a^{2} - \frac{169539079937}{19140625} a + \frac{72253187071}{19140625} \) |
\( \bigl[a\) , \( a^{2} - a + 1\) , \( 1\) , \( 2 a^{2} - 2 a - 5\) , \( 2 a^{2} - 4 a - 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-a+1\right){x}^{2}+\left(2a^{2}-2a-5\right){x}+2a^{2}-4a-4$ |
| 8855.2-C4 |
8855.2-C |
$8$ |
$16$ |
3.1.23.1 |
$3$ |
$[1, 1]$ |
8855.2 |
\( 5 \cdot 7 \cdot 11 \cdot 23 \) |
\( 5^{8} \cdot 7^{2} \cdot 11^{8} \cdot 23^{2} \) |
$1.94925$ |
$(a^2+1), (2a^2-a), (a^2+a-2), (3a^2-2a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$3.539083223$ |
1.475899729 |
\( \frac{1336472629257999049711}{94368148002734375} a^{2} - \frac{2195303670702484526999}{94368148002734375} a + \frac{1738059832571045383017}{94368148002734375} \) |
\( \bigl[a^{2} + 1\) , \( -a - 1\) , \( 0\) , \( -12 a^{2} + 50 a - 51\) , \( 126 a^{2} - 191 a + 125\bigr] \) |
${y}^2+\left(a^{2}+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a^{2}+50a-51\right){x}+126a^{2}-191a+125$ |
| 91.1-a3 |
91.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13^{4} \) |
$1.32661$ |
$(-a^2-a+2), (-2a^2+a+2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$145.8010047$ |
0.650897342 |
\( -\frac{3698907677516}{199927} a^{2} + \frac{293174005427}{28561} a + \frac{8312780816110}{199927} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -4\) , \( -3 a^{2} - a + 9\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}-4{x}-3a^{2}-a+9$ |
| 91.2-a6 |
91.2-a |
$8$ |
$16$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
91.2 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13^{4} \) |
$1.32661$ |
$(-a^2-a+2), (a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$145.8010047$ |
0.650897342 |
\( \frac{293174005427}{28561} a^{2} + \frac{1646689639527}{199927} a - \frac{1137252576911}{199927} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( -a^{2} + 4 a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-a^{2}+4a+4$ |
| 91.3-a7 |
91.3-a |
$8$ |
$16$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
91.3 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13^{4} \) |
$1.32661$ |
$(-a^2-a+2), (a^2-2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$145.8010047$ |
0.650897342 |
\( \frac{1646689639527}{199927} a^{2} - \frac{3698907677516}{199927} a + \frac{1320493859540}{199927} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} - 2\) , \( 1\) , \( a^{2} + 2 a - 4\) , \( a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{2}+2a-4\right){x}+a^{2}-2a+1$ |
| 40.1-a2 |
40.1-a |
$8$ |
$16$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{4} \) |
$2.01039$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$196.7319092$ |
1.010703957 |
\( \frac{33540448}{625} a^{2} - \frac{84221664}{625} a + \frac{25911744}{625} \) |
\( \bigl[a^{2} - 1\) , \( 1\) , \( 0\) , \( -98714 a^{2} - 115504 a + 45489\) , \( -3744636 a^{2} - 4381548 a + 1725570\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+{x}^{2}+\left(-98714a^{2}-115504a+45489\right){x}-3744636a^{2}-4381548a+1725570$ |
| 170.1-a7 |
170.1-a |
$8$ |
$16$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
170.1 |
\( 2 \cdot 5 \cdot 17 \) |
\( 2^{8} \cdot 5^{8} \cdot 17^{2} \) |
$2.55865$ |
$(a^2-a-2), (a^2-a-1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$51.08369406$ |
2.099526893 |
\( \frac{88730517357456201}{903125000} a^{2} + \frac{104099149160297057}{903125000} a - \frac{5058442147069184}{112890625} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 3\) , \( a + 1\) , \( 103 a^{2} - 84 a - 351\) , \( -934 a^{2} + 682 a + 3056\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(103a^{2}-84a-351\right){x}-934a^{2}+682a+3056$ |
| 182.1-i5 |
182.1-i |
$8$ |
$16$ |
3.3.229.1 |
$3$ |
$[3, 0]$ |
182.1 |
\( 2 \cdot 7 \cdot 13 \) |
\( 2^{8} \cdot 7^{2} \cdot 13^{4} \) |
$3.21910$ |
$(a+1), (-a^2+2), (2a^2-a-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.509499215$ |
$107.6807361$ |
2.719099234 |
\( -\frac{2543084227897}{358269184} a^{2} + \frac{226117619131}{358269184} a + \frac{11531334652291}{358269184} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 2\) , \( a + 1\) , \( -6 a^{2} - 13 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-6a^{2}-13a-1\right){x}$ |
| 2.2-a5 |
2.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{8} \) |
$1.78301$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$342.9545861$ |
0.602896961 |
\( \frac{130050481}{256} a^{2} + \frac{87514925}{128} a - \frac{54929731}{128} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a\) , \( 30965253611602296633 a^{2} - 16390422144515520442 a - 131575714394521753905\) , \( -112172935746444460857621319378 a^{2} + 59374994732320022090359795265 a + 476638568561218377704701696552\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(30965253611602296633a^{2}-16390422144515520442a-131575714394521753905\right){x}-112172935746444460857621319378a^{2}+59374994732320022090359795265a+476638568561218377704701696552$ |
| 68.1-b7 |
68.1-b |
$10$ |
$32$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
68.1 |
\( 2^{2} \cdot 17 \) |
\( 2^{16} \cdot 17^{4} \) |
$3.20923$ |
$(a), (-a+1), (-a^2-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$58.32536297$ |
3.281058009 |
\( \frac{38359531553}{21381376} a^{2} - \frac{9809524003}{10690688} a + \frac{19075559157}{10690688} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2621286038 a^{2} - 1387490161 a - 11138212765\) , \( -11948804891257 a^{2} + 6324700541666 a + 50772151245639\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2621286038a^{2}-1387490161a-11138212765\right){x}-11948804891257a^{2}+6324700541666a+50772151245639$ |
| 68.1-b10 |
68.1-b |
$10$ |
$32$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
68.1 |
\( 2^{2} \cdot 17 \) |
\( 2^{20} \cdot 17^{2} \) |
$3.20923$ |
$(a), (-a+1), (-a^2-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$116.6507259$ |
3.281058009 |
\( \frac{145085335090257}{18939904} a^{2} - \frac{206192002964659}{9469952} a + \frac{84948718183773}{9469952} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 294903105480143 a^{2} - 156097103262124 a - 1253084740315970\) , \( -4022779759545436614373 a^{2} + 2129324024934105364165 a + 17093356552251555630887\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(294903105480143a^{2}-156097103262124a-1253084740315970\right){x}-4022779759545436614373a^{2}+2129324024934105364165a+17093356552251555630887$ |
| 30.1-i2 |
30.1-i |
$8$ |
$16$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
30.1 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \) |
$4.55710$ |
$(-a^2+a+4), (a+2), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$31.93595523$ |
2.207736193 |
\( -\frac{574986201813697}{2700000000} a^{2} + \frac{89510335829221}{2700000000} a + \frac{1154474590344143}{900000000} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( 1\) , \( 3 a^{2} + 7 a - 40\) , \( -35 a^{2} + 37 a + 129\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(3a^{2}+7a-40\right){x}-35a^{2}+37a+129$ |
| 725.1-c6 |
725.1-c |
$8$ |
$16$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
725.1 |
\( 5^{2} \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.48087$ |
$(-a^3+a^2+4a-1), (-2a^3+2a^2+4a-1)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$825.6119082$ |
0.958201765 |
\( -\frac{5734972287}{4205} a^{3} + \frac{5734972287}{4205} a^{2} + \frac{11469944574}{4205} a + \frac{710427618}{841} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -5\) , \( -3 a^{3} + 3 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+{x}^{2}-5{x}-3a^{3}+3a^{2}+6a-2$ |
| 1519.1-g3 |
1519.1-g |
$8$ |
$16$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
1519.1 |
\( 7^{2} \cdot 31 \) |
\( 7^{8} \cdot 31^{2} \) |
$6.01177$ |
$(a^3-4a+1), (a^3-2a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.142922536$ |
$424.6798446$ |
2.253302277 |
\( \frac{10285978976492549}{2307361} a^{3} + \frac{11265387620368849}{2307361} a^{2} - \frac{7252470298494157}{2307361} a - \frac{4908256787630920}{2307361} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a\) , \( 13 a^{3} - 41 a^{2} + 24 a - 1\) , \( 149 a^{3} - 329 a^{2} - 29 a + 143\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(13a^{3}-41a^{2}+24a-1\right){x}+149a^{3}-329a^{2}-29a+143$ |
| 1519.3-g7 |
1519.3-g |
$8$ |
$16$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
1519.3 |
\( 7^{2} \cdot 31 \) |
\( 7^{8} \cdot 31^{2} \) |
$6.01177$ |
$(a^2-2a-3), (a^2+a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.142922536$ |
$424.6798446$ |
2.253302277 |
\( \frac{45156833227844888}{2307361} a^{3} - \frac{9529742832100898}{329623} a^{2} - \frac{103633154110180717}{2307361} a + \frac{94616697254305613}{2307361} \) |
\( \bigl[a^{2} - a\) , \( -a^{3} + 2 a^{2} - 3\) , \( a\) , \( -29 a^{3} + 15 a^{2} + 34 a - 41\) , \( 153 a^{3} - 12 a^{2} - 231 a + 96\bigr] \) |
${y}^2+\left(a^{2}-a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(-29a^{3}+15a^{2}+34a-41\right){x}+153a^{3}-12a^{2}-231a+96$ |
| 2025.1-d7 |
2025.1-d |
$10$ |
$32$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{16} \) |
$6.23176$ |
$(-2a^3+2a^2+4a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$61.57157232$ |
1.143355394 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 2025.1-d8 |
2025.1-d |
$10$ |
$32$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$6.23176$ |
$(-2a^3+2a^2+4a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$985.1451572$ |
1.143355394 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 3239.1-d2 |
3239.1-d |
$8$ |
$16$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
3239.1 |
\( 41 \cdot 79 \) |
\( 41^{4} \cdot 79^{2} \) |
$6.60859$ |
$(a^3-3a^2-a+4), (-3a^3+4a^2+5a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.041060128$ |
$549.8048880$ |
2.657207198 |
\( -\frac{1288562648705867280}{17635574401} a^{3} + \frac{361259142230026185}{17635574401} a^{2} + \frac{4157688447299560010}{17635574401} a + \frac{1762070327116760133}{17635574401} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - a\) , \( a\) , \( 16 a^{3} - 35 a^{2} - 6 a + 6\) , \( -4 a^{3} + 2 a^{2} + 14 a + 6\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-a\right){x}^{2}+\left(16a^{3}-35a^{2}-6a+6\right){x}-4a^{3}+2a^{2}+14a+6$ |
| 3239.4-d4 |
3239.4-d |
$8$ |
$16$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
3239.4 |
\( 41 \cdot 79 \) |
\( 41^{4} \cdot 79^{2} \) |
$6.60859$ |
$(2a^2-a-3), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.041060128$ |
$549.8048880$ |
2.657207198 |
\( -\frac{635303005293882925}{17635574401} a^{3} + \frac{1562606511769724020}{17635574401} a^{2} - \frac{309957139300059600}{17635574401} a - \frac{366580548898778797}{17635574401} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{2}\) , \( -12 a^{3} - 14 a^{2} + 9 a + 2\) , \( 33 a^{3} + 37 a^{2} - 25 a - 15\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-12a^{3}-14a^{2}+9a+2\right){x}+33a^{3}+37a^{2}-25a-15$ |
| 45.1-b7 |
45.1-b |
$10$ |
$32$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$4.82355$ |
$(-a-1), (-a^3+a^2+3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$61.57157232$ |
0.917854808 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
*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.
