| 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 |
| 26000.4-a1 |
26000.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{11} \cdot 5^{9} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.393755426$ |
$0.980855673$ |
3.089737953 |
\( -\frac{189329241}{65} a + \frac{135107663}{65} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 182 i + 66\) , \( 244 i + 896\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(182i+66\right){x}+244i+896$ |
| 26000.4-b1 |
26000.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{11} \cdot 5^{11} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.875708784$ |
1.751417569 |
\( \frac{1836351}{10985} a + \frac{19028007}{10985} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -48 i + 39\) , \( -29 i - 8\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-48i+39\right){x}-29i-8$ |
| 26000.4-c1 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.473143625$ |
$1.699559292$ |
3.216542584 |
\( -\frac{8646624}{4225} a - \frac{66027268}{4225} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 23 i + 13\) , \( -2 i + 59\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(23i+13\right){x}-2i+59$ |
| 26000.4-c2 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{11} \cdot 5^{8} \cdot 13^{8} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.118285906$ |
$0.424889823$ |
3.216542584 |
\( \frac{94078100761841}{20393268025} a - \frac{11284537597913}{20393268025} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -257 i - 197\) , \( 2392 i + 17\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-257i-197\right){x}+2392i+17$ |
| 26000.4-c3 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{10} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.236571812$ |
$0.849779646$ |
3.216542584 |
\( -\frac{15461171586}{17850625} a - \frac{9080741152}{17850625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -7 i + 53\) , \( 192 i + 117\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-7i+53\right){x}+192i+117$ |
| 26000.4-c4 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{7} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.946287251$ |
$3.399118585$ |
3.216542584 |
\( \frac{75008}{65} a - \frac{29104}{65} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 3 i - 2\) , \( 3 i - 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(3i-2\right){x}+3i-2$ |
| 26000.4-c5 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{11} \cdot 5^{14} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.473143625$ |
$0.424889823$ |
3.216542584 |
\( \frac{143087370512191}{66015625} a + \frac{29292377558137}{66015625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -237 i + 943\) , \( 10728 i + 4169\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-237i+943\right){x}+10728i+4169$ |
| 26000.4-c6 |
26000.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{7} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.946287251$ |
$0.849779646$ |
3.216542584 |
\( \frac{4355686402}{65} a + \frac{17124606704}{65} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 373 i + 213\) , \( 12 i - 3489\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(373i+213\right){x}+12i-3489$ |
| 26000.4-d1 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{9} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.568858194$ |
$1.430043658$ |
3.253968216 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -32 i + 59\) , \( 177 i + 155\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-32i+59\right){x}+177i+155$ |
| 26000.4-d2 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{15} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.568858194$ |
$0.715021829$ |
3.253968216 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -79 i - 204\) , \( 570 i + 1169\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-79i-204\right){x}+570i+1169$ |
| 26000.4-d3 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.137716389$ |
$1.430043658$ |
3.253968216 |
\( -\frac{34602624}{105625} a + \frac{89434832}{105625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( i - 19\) , \( 21 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(i-19\right){x}+21i+1$ |
| 26000.4-d4 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{12} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.568858194$ |
$0.715021829$ |
3.253968216 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( i + 106\) , \( 346 i - 99\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(i+106\right){x}+346i-99$ |
| 26000.4-d5 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{8} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.284429097$ |
$0.357510914$ |
3.253968216 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -99 i + 656\) , \( -5844 i - 1679\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-99i+656\right){x}-5844i-1679$ |
| 26000.4-d6 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{15} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.137716389$ |
$0.357510914$ |
3.253968216 |
\( \frac{286134796876244}{66015625} a + \frac{251971335359842}{66015625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 101 i + 1556\) , \( 24336 i - 2919\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(101i+1556\right){x}+24336i-2919$ |
| 26000.4-e1 |
26000.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{11} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.657708415$ |
$1.233578115$ |
3.245338832 |
\( \frac{12853728}{4225} a - \frac{529954704}{4225} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 68 i - 31\) , \( -261 i - 73\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(68i-31\right){x}-261i-73$ |
| 26000.4-e2 |
26000.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.315416831$ |
$1.233578115$ |
3.245338832 |
\( -\frac{1492992}{8125} a + \frac{4755456}{8125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -22 i - 4\) , \( -38 i - 41\bigr] \) |
${y}^2={x}^{3}+\left(-22i-4\right){x}-38i-41$ |
| 26000.4-f1 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{16} \cdot 5^{13} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.215620255$ |
1.293721531 |
\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -1590 i - 5230\) , \( -65256 i - 139092\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1590i-5230\right){x}-65256i-139092$ |
| 26000.4-f2 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{24} \cdot 5^{11} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.646860765$ |
1.293721531 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 10 i - 30\) , \( -296 i - 372\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(10i-30\right){x}-296i-372$ |
| 26000.4-f3 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{31} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.053905063$ |
1.293721531 |
\( -\frac{94290382838862669189021}{261902809143066406250} a + \frac{23228384730714798359947}{261902809143066406250} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -3370 i + 9310\) , \( -201360 i - 785020\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-3370i+9310\right){x}-201360i-785020$ |
| 26000.4-f4 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{15} \cdot 5^{20} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.161715191$ |
1.293721531 |
\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -1150 i + 1850\) , \( -21384 i - 19388\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1150i+1850\right){x}-21384i-19388$ |
| 26000.4-f5 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{14} \cdot 5^{20} \cdot 13^{6} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.107810127$ |
1.293721531 |
\( \frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -1470 i - 5390\) , \( 71000 i + 128500\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1470i-5390\right){x}+71000i+128500$ |
| 26000.4-f6 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{16} \cdot 13^{12} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.053905063$ |
1.293721531 |
\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 2350 i - 22650\) , \( 307616 i - 1202388\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2350i-22650\right){x}+307616i-1202388$ |
| 26000.4-f7 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{18} \cdot 5^{16} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.323430382$ |
1.293721531 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -470 i + 610\) , \( 4200 i + 6900\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-470i+610\right){x}+4200i+6900$ |
| 26000.4-f8 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{15} \cdot 5^{17} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.161715191$ |
1.293721531 |
\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -7470 i + 9610\) , \( -282200 i - 436900\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-7470i+9610\right){x}-282200i-436900$ |
| 26000.4-g1 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{30} \cdot 5^{15} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.473430659$ |
$0.214824951$ |
3.661369868 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -1880 i + 828\) , \( 5448 i - 35920\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-1880i+828\right){x}+5448i-35920$ |
| 26000.4-g2 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.157810219$ |
$0.644474854$ |
3.661369868 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -40 i + 208\) , \( 1120 i + 384\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-40i+208\right){x}+1120i+384$ |
| 26000.4-g3 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{15} \cdot 5^{12} \cdot 13^{6} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.078905109$ |
$0.322237427$ |
3.661369868 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 240 i + 168\) , \( 1808 i + 3600\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(240i+168\right){x}+1808i+3600$ |
| 26000.4-g4 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{21} \cdot 5^{24} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.236715329$ |
$0.107412475$ |
3.661369868 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -2200 i - 1412\) , \( -63800 i - 79056\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2200i-1412\right){x}-63800i-79056$ |
| 26000.4-g5 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{14} \cdot 5^{7} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.473430659$ |
$1.933424563$ |
3.661369868 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -12\) , \( 8 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}-12{x}+8i$ |
| 26000.4-g6 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{8} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.236715329$ |
$0.966712281$ |
3.661369868 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -20 i - 152\) , \( 160 i + 664\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-20i-152\right){x}+160i+664$ |
| 26000.4-h1 |
26000.4-h |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{15} \cdot 5^{5} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.066456528$ |
$2.362913116$ |
3.768744045 |
\( \frac{2124209}{6500} a - \frac{5592087}{6500} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -6 i - 2\) , \( 8 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-6i-2\right){x}+8i-4$ |
| 26000.4-h2 |
26000.4-h |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{11} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.022152176$ |
$0.787637705$ |
3.768744045 |
\( -\frac{1498457535463}{8582031250} a + \frac{5584902421359}{8582031250} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 54 i + 18\) , \( -160 i + 100\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(54i+18\right){x}-160i+100$ |
| 26000.4-i1 |
26000.4-i |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{29} \cdot 5^{5} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.050619341$ |
2.101238683 |
\( \frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 8 i + 34\) , \( -94 i + 68\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(8i+34\right){x}-94i+68$ |
| 26000.4-j1 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.752555139$ |
$0.533168923$ |
4.001491570 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -191 i - 637\) , \( 2970 i + 6165\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-191i-637\right){x}+2970i+6165$ |
| 26000.4-j2 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.938138784$ |
$1.066337847$ |
4.001491570 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 66 i + 24\) , \( -36 i - 235\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(66i+24\right){x}-36i-235$ |
| 26000.4-j3 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{12} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.250851713$ |
$0.177722974$ |
4.001491570 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 219 i + 233\) , \( 11702 i + 20389\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(219i+233\right){x}+11702i+20389$ |
| 26000.4-j4 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1.876277569$ |
$1.066337847$ |
4.001491570 |
\( -\frac{4789923264}{2640625} a + \frac{673064048}{2640625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -16 i - 37\) , \( 35 i + 120\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-16i-37\right){x}+35i+120$ |
| 26000.4-j5 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{19} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$3.752555139$ |
$0.533168923$ |
4.001491570 |
\( \frac{6814517046148}{3173828125} a + \frac{1205241786064}{3173828125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 159 i + 63\) , \( 450 i + 775\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(159i+63\right){x}+450i+775$ |
| 26000.4-j6 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{19} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.312712928$ |
$0.355445949$ |
4.001491570 |
\( \frac{107236037214208}{536376953125} a + \frac{978770751225856}{536376953125} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -374 i - 56\) , \( 332 i - 759\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-374i-56\right){x}+332i-759$ |
| 26000.4-j7 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{14} \cdot 13^{6} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.625425856$ |
$0.355445949$ |
4.001491570 |
\( -\frac{4259875740810816}{75418890625} a + \frac{6940682724261488}{75418890625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 844 i + 233\) , \( 3327 i + 9264\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(844i+233\right){x}+3327i+9264$ |
| 26000.4-j8 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.250851713$ |
$0.177722974$ |
4.001491570 |
\( -\frac{14159685840327748}{1373125} a + \frac{7060801251114256}{1373125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 13469 i + 3733\) , \( 230702 i + 591639\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(13469i+3733\right){x}+230702i+591639$ |
*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.
