| 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 |
| 23716.6-a1 |
23716.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{8} \cdot 11^{4} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.383868981$ |
0.870533023 |
\( \frac{14992796757}{32768} a - \frac{12982304015}{16384} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 238 a + 867\) , \( -8297 a + 10004\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(238a+867\right){x}-8297a+10004$ |
| 23716.6-a2 |
23716.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{8} \cdot 11^{4} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$1.151606943$ |
0.870533023 |
\( \frac{51957}{32} a - \frac{35111}{16} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 28 a - 8\) , \( -44 a - 76\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(28a-8\right){x}-44a-76$ |
| 23716.6-b1 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1.085177090$ |
$0.191554991$ |
2.514172357 |
\( -\frac{2775668240489}{85184} a - \frac{5083125111585}{85184} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -2413 a + 7986\) , \( -151201 a - 79460\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2413a+7986\right){x}-151201a-79460$ |
| 23716.6-b2 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{7} \cdot 7^{6} \cdot 11^{18} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$4.340708360$ |
$0.095777495$ |
2.514172357 |
\( \frac{41728910180660407}{200859416110144} a - \frac{51818768961625453}{200859416110144} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -2068 a + 2179\) , \( -29911 a - 131211\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2068a+2179\right){x}-29911a-131211$ |
| 23716.6-b3 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{25} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.340708360$ |
$0.191554991$ |
2.514172357 |
\( \frac{74168468086089}{22330474496} a + \frac{16633019348749}{22330474496} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 206 a - 1715\) , \( -1801 a + 23741\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(206a-1715\right){x}-1801a+23741$ |
| 23716.6-b4 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{6} \cdot 11^{7} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.361725696$ |
$0.574664973$ |
2.514172357 |
\( -\frac{2222449}{45056} a + \frac{22133027}{22528} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -68 a + 111\) , \( -337 a + 284\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-68a+111\right){x}-337a+284$ |
| 23716.6-b5 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.723451393$ |
$0.574664973$ |
2.514172357 |
\( \frac{998361}{7744} a + \frac{11225095}{3872} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -73 a - 96\) , \( -364 a - 52\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-73a-96\right){x}-364a-52$ |
| 23716.6-b6 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{6} \cdot 11^{12} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$2.170354180$ |
$0.191554991$ |
2.514172357 |
\( -\frac{49453830610989}{7256313856} a + \frac{47470228116479}{7256313856} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 1222 a + 359\) , \( 2905 a - 32875\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1222a+359\right){x}+2905a-32875$ |
| 23716.6-b7 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{6} \cdot 11^{7} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.446902786$ |
$0.574664973$ |
2.514172357 |
\( -\frac{7153263}{2816} a + \frac{88973461}{2816} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -179 a + 210\) , \( -170 a + 1880\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-179a+210\right){x}-170a+1880$ |
| 23716.6-b8 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.446902786$ |
$0.287332486$ |
2.514172357 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -1053 a - 1356\) , \( -27440 a - 10664\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1053a-1356\right){x}-27440a-10664$ |
| 23716.6-c1 |
23716.6-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{4} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.786053931$ |
1.188401839 |
\( -\frac{1804271}{256} a + \frac{1450869}{256} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 84 a - 57\) , \( -247 a - 216\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(84a-57\right){x}-247a-216$ |
| 23716.6-c2 |
23716.6-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{4} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.262017977$ |
1.188401839 |
\( \frac{244445227817}{16777216} a + \frac{134763989101}{16777216} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -266 a + 1308\) , \( -10922 a - 510\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-266a+1308\right){x}-10922a-510$ |
| 23716.6-d1 |
23716.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{10} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$0.985370750$ |
1.489740546 |
\( -\frac{1804271}{256} a + \frac{1450869}{256} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 8 a - 75\) , \( 30 a - 231\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-75\right){x}+30a-231$ |
| 23716.6-d2 |
23716.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{10} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.328456916$ |
1.489740546 |
\( \frac{244445227817}{16777216} a + \frac{134763989101}{16777216} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 498 a + 170\) , \( 324 a - 8708\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(498a+170\right){x}+324a-8708$ |
| 23716.6-e1 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{36} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9550 a - 8356\) , \( 406356 a + 14472\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9550a-8356\right){x}+406356a+14472$ |
| 23716.6-e2 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -414 a + 1420\) , \( 11079 a + 5250\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-414a+1420\right){x}+11079a+5250$ |
| 23716.6-e3 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -833 a - 329\) , \( 13391 a - 4613\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-833a-329\right){x}+13391a-4613$ |
| 23716.6-e4 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -63 a + 56\) , \( -105 a + 420\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-63a+56\right){x}-105a+420$ |
| 23716.6-e5 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -64 a + 55\) , \( 103 a - 392\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-64a+55\right){x}+103a-392$ |
| 23716.6-e6 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 30 a - 26\) , \( -148 a + 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-26\right){x}-148a+24$ |
| 23716.6-e7 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -250 a + 219\) , \( 2988 a - 179\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-250a+219\right){x}+2988a-179$ |
| 23716.6-e8 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{45} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 706 a - 3795\) , \( 63187 a + 28686\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(706a-3795\right){x}+63187a+28686$ |
| 23716.6-e9 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{45} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1967 a + 1456\) , \( 78169 a - 27202\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1967a+1456\right){x}+78169a-27202$ |
| 23716.6-e10 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{18} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.149644562$ |
2.714895745 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 1990 a - 1741\) , \( 31212 a + 2229\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1990a-1741\right){x}+31212a+2229$ |
| 23716.6-e11 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.448933686$ |
2.714895745 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 590 a - 516\) , \( -6420 a + 430\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(590a-516\right){x}-6420a+430$ |
| 23716.6-e12 |
23716.6-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.049881520$ |
2.714895745 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 152910 a - 133796\) , \( 26096468 a + 519816\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(152910a-133796\right){x}+26096468a+519816$ |
| 23716.6-f1 |
23716.6-f |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{2} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$0.306221512$ |
3.472225579 |
\( \frac{14992796757}{32768} a - \frac{12982304015}{16384} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -1026 a + 1411\) , \( 1559 a + 23744\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-1026a+1411\right){x}+1559a+23744$ |
| 23716.6-f2 |
23716.6-f |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 5 \) |
$1$ |
$0.918664538$ |
3.472225579 |
\( \frac{51957}{32} a - \frac{35111}{16} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 4 a + 56\) , \( -173 a + 152\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a+56\right){x}-173a+152$ |
| 23716.6-g1 |
23716.6-g |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{35} \cdot 7^{8} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$5.427371109$ |
$0.095007311$ |
4.677445842 |
\( -\frac{3249994516225}{8589934592} a - \frac{16462660840237}{4294967296} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 2160 a + 4427\) , \( -127480 a + 208333\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(2160a+4427\right){x}-127480a+208333$ |
| 23716.6-g2 |
23716.6-g |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{17} \cdot 7^{8} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.809123703$ |
$0.285021933$ |
4.677445842 |
\( \frac{89671}{2048} a + \frac{1477803}{1024} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -185 a - 403\) , \( 1159 a - 1737\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-185a-403\right){x}+1159a-1737$ |
| 23716.6-h1 |
23716.6-h |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.001846424$ |
3.026507316 |
\( \frac{16471}{4} a - 3375 \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 11 a - 5\) , \( -13 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(11a-5\right){x}-13a-9$ |
| 23716.6-h2 |
23716.6-h |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.001846424$ |
3.026507316 |
\( -\frac{16471}{4} a + \frac{2971}{4} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 9 a - 14\) , \( -13 a + 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-14\right){x}-13a+9$ |
| 23716.6-h3 |
23716.6-h |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{21} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.285978060$ |
3.026507316 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -179 a + 615\) , \( 1167 a - 739\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-179a+615\right){x}+1167a-739$ |
| 23716.6-h4 |
23716.6-h |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{21} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.285978060$ |
3.026507316 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -361 a - 144\) , \( 787 a + 519\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-361a-144\right){x}+787a+519$ |
| 23716.6-i1 |
23716.6-i |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{35} \cdot 7^{2} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 11 \) |
$0.123209096$ |
$0.833685772$ |
10.24943837 |
\( -\frac{3249994516225}{8589934592} a - \frac{16462660840237}{4294967296} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 60 a - 47\) , \( 200 a + 101\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(60a-47\right){x}+200a+101$ |
| 23716.6-i2 |
23716.6-i |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{17} \cdot 7^{2} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 11 \) |
$0.041069698$ |
$2.501057318$ |
10.24943837 |
\( \frac{89671}{2048} a + \frac{1477803}{1024} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -5 a + 3\) , \( -a - 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+3\right){x}-a-5$ |
*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.
