| 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 |
| 99372.4-a1 |
99372.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 7^{3} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.245999614$ |
1.136223551 |
\( \frac{56875979215}{47628} a - \frac{14078637859}{15876} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3006 a + 1195\) , \( 47825 a - 52288\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-3006a+1195\right){x}+47825a-52288$ |
| 99372.4-a2 |
99372.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.491999229$ |
1.136223551 |
\( -\frac{16953431}{21168} a + \frac{527893}{1323} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -166 a + 95\) , \( 1149 a - 852\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-166a+95\right){x}+1149a-852$ |
| 99372.4-b1 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{19} \cdot 13^{7} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{3} \) |
$1$ |
$0.057832981$ |
1.202035947 |
\( -\frac{81099357856043750896541}{254032521274030044} a - \frac{756257117794683381014315}{254032521274030044} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 63237 a - 37217\) , \( -4634337 a - 606780\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(63237a-37217\right){x}-4634337a-606780$ |
| 99372.4-b2 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \cdot 13^{24} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.028916490$ |
1.202035947 |
\( \frac{1238994426135721563920288123}{16530944821937736789963} a - \frac{3235581081186234554256911065}{33061889643875473579926} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 90957 a - 145807\) , \( 17081443 a - 18174670\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(90957a-145807\right){x}+17081443a-18174670$ |
| 99372.4-b3 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{19} \cdot 13^{8} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.028916490$ |
1.202035947 |
\( \frac{1710733168139618453447801}{70451685899997665536} a - \frac{8927812032065273021095625}{422710115399985993216} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 6057 a + 95768\) , \( -13993919 a + 8365475\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(6057a+95768\right){x}-13993919a+8365475$ |
| 99372.4-b4 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{3} \cdot 7^{9} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.173498944$ |
1.202035947 |
\( \frac{40759196411725}{18610189416} a - \frac{46842802400791}{148881515328} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 1297 a - 1777\) , \( 19787 a - 27700\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(1297a-1777\right){x}+19787a-27700$ |
| 99372.4-b5 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{36} \cdot 3 \cdot 7^{11} \cdot 13^{7} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.057832981$ |
1.202035947 |
\( -\frac{107417497830800029}{51569972772864} a + \frac{787851936733685797}{412559782182912} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -9303 a + 16408\) , \( 163905 a + 552867\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-9303a+16408\right){x}+163905a+552867$ |
| 99372.4-b6 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{3} \cdot 13^{8} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$1$ |
$0.260248416$ |
1.202035947 |
\( -\frac{5302115243}{12073698} a + \frac{694365562771}{325989846} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -813 a + 278\) , \( -3845 a + 1907\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-813a+278\right){x}-3845a+1907$ |
| 99372.4-b7 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{9} \cdot 13^{12} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.086749472$ |
1.202035947 |
\( -\frac{151053045516501325}{6814431024492} a + \frac{268398648679382443}{122659758440856} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 12417 a - 7417\) , \( -405173 a - 62380\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(12417a-7417\right){x}-405173a-62380$ |
| 99372.4-b8 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{9} \cdot 7^{3} \cdot 13^{7} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.520496833$ |
1.202035947 |
\( \frac{35160325189}{619164} a + \frac{4563294370}{154791} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -443 a + 218\) , \( 2393 a - 3325\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-443a+218\right){x}+2393a-3325$ |
| 99372.4-b9 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{3} \cdot 13^{15} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{3} \) |
$1$ |
$0.057832981$ |
1.202035947 |
\( -\frac{14285238281043392612006}{1558861407831} a + \frac{25600960828854981933859}{6235445631324} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 90897 a - 146117\) , \( 17060979 a - 18066672\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(90897a-146117\right){x}+17060979a-18066672$ |
| 99372.4-b10 |
99372.4-b |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{11} \cdot 13^{8} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.028916490$ |
1.202035947 |
\( \frac{81968147518467806744117}{40918557498} a + \frac{59775831478923938886143}{6819759583} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 1011867 a - 595507\) , \( -296390015 a - 39685318\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(1011867a-595507\right){x}-296390015a-39685318$ |
| 99372.4-c1 |
99372.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{4} \cdot 13^{8} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.500939236$ |
1.156869613 |
\( -\frac{538194227}{111132} a - \frac{175455025}{55566} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -236 a + 270\) , \( -320 a - 1485\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-236a+270\right){x}-320a-1485$ |
| 99372.4-d1 |
99372.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{6} \cdot 13^{7} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.215016812$ |
1.986240230 |
\( \frac{27347390144674}{22754277} a - \frac{51564689774159}{45508554} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -294 a - 3316\) , \( -10400 a - 74101\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-294a-3316\right){x}-10400a-74101$ |
| 99372.4-d2 |
99372.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{3} \cdot 7^{9} \cdot 13^{10} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.215016812$ |
1.986240230 |
\( \frac{79050326992150}{1481836332249} a - \frac{90478870211462581}{2963672664498} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -2074 a + 444\) , \( 35156 a - 27445\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2074a+444\right){x}+35156a-27445$ |
| 99372.4-d3 |
99372.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{3} \cdot 13^{7} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.860067248$ |
1.986240230 |
\( \frac{26497139}{5733} a - \frac{44693227}{91728} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 76 a + 4\) , \( -18 a - 237\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(76a+4\right){x}-18a-237$ |
| 99372.4-d4 |
99372.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 13^{8} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.430033624$ |
1.986240230 |
\( -\frac{9912006110}{10955763} a + \frac{2578613923}{4869228} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -64 a - 156\) , \( 314 a - 1789\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-64a-156\right){x}+314a-1789$ |
| 99372.4-e1 |
99372.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{7} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.269250960$ |
1.865425377 |
\( \frac{408415775}{777924} a + \frac{241158518}{194481} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 547 a - 685\) , \( -1414 a + 3775\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(547a-685\right){x}-1414a+3775$ |
| 99372.4-e2 |
99372.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{14} \cdot 7^{8} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.134625480$ |
1.865425377 |
\( -\frac{321426784225}{514596726} a + \frac{370102537351}{171532242} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -2613 a + 2705\) , \( -16294 a + 33365\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2613a+2705\right){x}-16294a+33365$ |
| 99372.4-f1 |
99372.4-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{14} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.151020233$ |
$0.312234159$ |
4.355869974 |
\( \frac{6173894787503057}{1694851494} a - \frac{278042704444494}{282475249} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -1842 a - 108\) , \( 36018 a - 15837\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1842a-108\right){x}+36018a-15837$ |
| 99372.4-f2 |
99372.4-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{13} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.075510116$ |
$0.624468319$ |
4.355869974 |
\( \frac{82172737747}{69177612} a + \frac{115516717957}{69177612} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -122 a - 18\) , \( 410 a - 279\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-122a-18\right){x}+410a-279$ |
| 99372.4-g1 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.632376205$ |
$0.760041148$ |
4.439887655 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -31 a + 60\) , \( 243 a + 152\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a+60\right){x}+243a+152$ |
| 99372.4-g2 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 3089 a - 5790\) , \( 40575 a + 15536\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3089a-5790\right){x}+40575a+15536$ |
| 99372.4-g3 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$0.158094051$ |
$0.190010287$ |
4.439887655 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -831 a + 1560\) , \( 5099 a + 3384\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-831a+1560\right){x}+5099a+3384$ |
| 99372.4-g4 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7311 a + 13710\) , \( -380137 a - 170928\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7311a+13710\right){x}-380137a-170928$ |
| 99372.4-g5 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.380020574$ |
4.439887655 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -671 a + 1260\) , \( 10579 a + 5784\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-671a+1260\right){x}+10579a+5784$ |
| 99372.4-g6 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$0.632376205$ |
$0.190010287$ |
4.439887655 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10751 a + 20160\) , \( 681403 a + 334392\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10751a+20160\right){x}+681403a+334392$ |
| 99372.4-h1 |
99372.4-h |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{4} \cdot 13^{2} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.027508727$ |
$1.806162104$ |
4.819210287 |
\( -\frac{538194227}{111132} a - \frac{175455025}{55566} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 14 a + 9\) , \( 12 a - 42\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a+9\right){x}+12a-42$ |
| 99372.4-i1 |
99372.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{7} \cdot 13^{11} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.609523116$ |
$0.287921117$ |
4.863448373 |
\( \frac{1406393503000237}{524187001884} a - \frac{621847336368386}{131046750471} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -299 a + 778\) , \( -8127 a + 215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-299a+778\right){x}-8127a+215$ |
| 99372.4-i2 |
99372.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{5} \cdot 13^{16} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.219046233$ |
$0.143960558$ |
4.863448373 |
\( -\frac{210601872762588523}{283712776225242} a - \frac{138310027490714181}{94570925408414} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 2481 a - 632\) , \( -18607 a - 43679\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(2481a-632\right){x}-18607a-43679$ |
| 99372.4-j1 |
99372.4-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{14} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.086598174$ |
1.999899181 |
\( \frac{6173894787503057}{1694851494} a - \frac{278042704444494}{282475249} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 12019 a + 16360\) , \( 1355219 a - 1594281\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12019a+16360\right){x}+1355219a-1594281$ |
| 99372.4-j2 |
99372.4-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{13} \cdot 13^{9} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.173196349$ |
1.999899181 |
\( \frac{82172737747}{69177612} a + \frac{115516717957}{69177612} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 699 a + 1250\) , \( 12973 a - 21477\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(699a+1250\right){x}+12973a-21477$ |
| 99372.4-k1 |
99372.4-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 7^{7} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \) |
$0.025937005$ |
$0.970798145$ |
4.884582136 |
\( \frac{408415775}{777924} a + \frac{241158518}{194481} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 55 a - 38\) , \( -57 a + 37\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(55a-38\right){x}-57a+37$ |
| 99372.4-k2 |
99372.4-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{14} \cdot 7^{8} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \) |
$0.051874010$ |
$0.485399072$ |
4.884582136 |
\( -\frac{321426784225}{514596726} a + \frac{370102537351}{171532242} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -235 a + 132\) , \( -757 a + 667\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-235a+132\right){x}-757a+667$ |
| 99372.4-l1 |
99372.4-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 7^{3} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.137500230$ |
$0.886964225$ |
5.632988827 |
\( \frac{56875979215}{47628} a - \frac{14078637859}{15876} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -18 a + 210\) , \( 1204 a - 561\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-18a+210\right){x}+1204a-561$ |
| 99372.4-l2 |
99372.4-l |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 13^{3} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.068750115$ |
$1.773928451$ |
5.632988827 |
\( -\frac{16953431}{21168} a + \frac{527893}{1323} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a + 10\) , \( 20 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+10\right){x}+20a-5$ |
*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.
