| 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 |
| 52000.5-a1 |
52000.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{3} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.215561221$ |
$4.408756167$ |
3.801427458 |
\( -\frac{1374}{65} a + \frac{116018}{65} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( i + 1\) , \( -1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(i+1\right){x}-1$ |
| 52000.5-b1 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.621322125$ |
$0.532258081$ |
3.451847214 |
\( \frac{363114750592}{4225} a - \frac{51978449984}{4225} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -68 i + 968\) , \( 11542 i + 1544\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-68i+968\right){x}+11542i+1544$ |
| 52000.5-b2 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{18} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.242644250$ |
$0.266129040$ |
3.451847214 |
\( -\frac{139247548851818}{5078125} a - \frac{4765670334626}{5078125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -1463 i + 3076\) , \( -59130 i - 45519\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-1463i+3076\right){x}-59130i-45519$ |
| 52000.5-b3 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{9} \cdot 13^{8} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.405330531$ |
$0.532258081$ |
3.451847214 |
\( -\frac{4367603145928}{20393268025} a + \frac{514683042256}{20393268025} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 55 i - 64\) , \( -868 i - 266\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(55i-64\right){x}-868i-266$ |
| 52000.5-b4 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{24} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.242644250$ |
$0.266129040$ |
3.451847214 |
\( \frac{778063252549418}{1983642578125} a + \frac{463325304434674}{1983642578125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -33 i - 434\) , \( -5764 i - 3381\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-33i-434\right){x}-5764i-3381$ |
| 52000.5-b5 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{18} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.621322125$ |
$0.532258081$ |
3.451847214 |
\( -\frac{246826028856}{66015625} a + \frac{291128921792}{66015625} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -88 i + 201\) , \( -755 i - 644\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-88i+201\right){x}-755i-644$ |
| 52000.5-b6 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{12} \cdot 13^{4} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.810661062$ |
$0.532258081$ |
3.451847214 |
\( \frac{125379433344}{17850625} a + \frac{122487180992}{17850625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 22 i - 246\) , \( -6 i + 1408\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(22i-246\right){x}-6i+1408$ |
| 52000.5-c1 |
52000.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{15} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.642527931$ |
2.570111724 |
\( \frac{959507758902}{5078125} a - \frac{410040476086}{5078125} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -291 i - 70\) , \( -1717 i + 903\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-291i-70\right){x}-1717i+903$ |
| 52000.5-c2 |
52000.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{9} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.285055862$ |
2.570111724 |
\( -\frac{24755584}{325} a - \frac{19408448}{325} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 28 i - 59\) , \( 101 i - 149\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(28i-59\right){x}+101i-149$ |
| 52000.5-c3 |
52000.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{12} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.285055862$ |
2.570111724 |
\( -\frac{11655336}{105625} a + \frac{23620448}{105625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -16 i + 5\) , \( -52 i - 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-16i+5\right){x}-52i-2$ |
| 52000.5-c4 |
52000.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{12} \cdot 13^{4} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.642527931$ |
2.570111724 |
\( \frac{36855806386}{17850625} a + \frac{134629168798}{17850625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 139 i - 80\) , \( -763 i + 25\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(139i-80\right){x}-763i+25$ |
| 52000.5-d1 |
52000.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{8} \cdot 13^{6} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.701269099$ |
$0.772818770$ |
4.335631386 |
\( \frac{41546262094}{120670225} a + \frac{205320721442}{120670225} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 31 i - 72\) , \( -114\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(31i-72\right){x}-114$ |
| 52000.5-d2 |
52000.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{7} \cdot 13^{3} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.402538198$ |
$1.545637541$ |
4.335631386 |
\( -\frac{904474088}{10985} a + \frac{641656096}{10985} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 26 i - 37\) , \( 90 i - 73\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(26i-37\right){x}+90i-73$ |
| 52000.5-e1 |
52000.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{17} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.576732977$ |
2.306931910 |
\( \frac{428516992}{5078125} a + \frac{527147456}{5078125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 62 i + 8\) , \( -624 i + 156\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(62i+8\right){x}-624i+156$ |
| 52000.5-e2 |
52000.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{13} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.576732977$ |
2.306931910 |
\( -\frac{19043187328}{105625} a + \frac{1934453696}{105625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -328 i + 154\) , \( 294 i - 2742\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-328i+154\right){x}+294i-2742$ |
| 52000.5-f1 |
52000.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{11} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.099440846$ |
$1.289614142$ |
4.103690288 |
\( \frac{428516992}{5078125} a + \frac{527147456}{5078125} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -8 i + 9\) , \( 59 i - 9\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-8i+9\right){x}+59i-9$ |
| 52000.5-f2 |
52000.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{7} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.198881692$ |
$1.289614142$ |
4.103690288 |
\( -\frac{19043187328}{105625} a + \frac{1934453696}{105625} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 14 i - 71\) , \( -101 i + 245\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(14i-71\right){x}-101i+245$ |
| 52000.5-g1 |
52000.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{4} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.603639602$ |
$0.877696423$ |
4.238498565 |
\( \frac{170823808}{714025} a + \frac{756097984}{714025} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 48 i + 22\) , \( -126 i - 2\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(48i+22\right){x}-126i-2$ |
| 52000.5-g2 |
52000.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{12} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.301819801$ |
$0.877696423$ |
4.238498565 |
\( -\frac{54739584}{105625} a + \frac{278314688}{105625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 58 i + 36\) , \( 8 i - 144\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(58i+36\right){x}+8i-144$ |
| 52000.5-g3 |
52000.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{15} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.603639602$ |
$0.877696423$ |
4.238498565 |
\( \frac{72142218728}{5078125} a + \frac{166548601504}{5078125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -108 i - 49\) , \( 466 i - 55\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-108i-49\right){x}+466i-55$ |
| 52000.5-g4 |
52000.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{12} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.603639602$ |
$0.877696423$ |
4.238498565 |
\( -\frac{16041806568}{8125} a + \frac{23413439024}{8125} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -202 i - 134\) , \( 1468 i + 101\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-202i-134\right){x}+1468i+101$ |
| 52000.5-h1 |
52000.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{13} \cdot 13^{4} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.276496286$ |
2.211970294 |
\( -\frac{306369913373848}{17850625} a - \frac{2142057330263024}{17850625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -1663 i + 3336\) , \( -67920 i - 56249\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-1663i+3336\right){x}-67920i-56249$ |
| 52000.5-h2 |
52000.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{25} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.276496286$ |
2.211970294 |
\( \frac{383712134285368}{1983642578125} a - \frac{480402061726976}{1983642578125} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -217 i - 279\) , \( -6144 i - 1890\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-217i-279\right){x}-6144i-1890$ |
| 52000.5-h3 |
52000.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{20} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.276496286$ |
2.211970294 |
\( -\frac{723822505344}{66015625} a + \frac{100772067008}{66015625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 398 i - 844\) , \( 7492 i - 8356\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(398i-844\right){x}+7492i-8356$ |
| 52000.5-h4 |
52000.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{22} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.276496286$ |
2.211970294 |
\( \frac{11876976934272}{3173828125} a + \frac{5317173197504}{3173828125} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 88 i + 742\) , \( 7186 i - 2918\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(88i+742\right){x}+7186i-2918$ |
| 52000.5-i1 |
52000.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{10} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.269556819$ |
$1.078073649$ |
4.649633659 |
\( \frac{9109431098}{8125} a - \frac{703641086}{8125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 101 i + 93\) , \( -180 i + 635\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(101i+93\right){x}-180i+635$ |
| 52000.5-i2 |
52000.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{8} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.539113638$ |
$2.156147299$ |
4.649633659 |
\( \frac{2630664}{4225} a + \frac{6709952}{4225} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 6 i + 8\) , \( 2 i + 11\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(6i+8\right){x}+2i+11$ |
| 52000.5-i3 |
52000.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{7} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.078227276$ |
$2.156147299$ |
4.649633659 |
\( -\frac{42112}{65} a + \frac{108224}{65} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 4 i + 9\) , \( -9 i + 5\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(4i+9\right){x}-9i+5$ |
| 52000.5-i4 |
52000.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{7} \cdot 13^{4} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.078227276$ |
$1.078073649$ |
4.649633659 |
\( -\frac{9896441706}{142805} a + \frac{2615329822}{142805} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 31 i + 83\) , \( 272 i - 129\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(31i+83\right){x}+272i-129$ |
| 52000.5-j1 |
52000.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{7} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.112319589$ |
3.112319589 |
\( -\frac{3752}{65} a - \frac{7136}{65} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -2 i - 1\) , \( 3 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-2i-1\right){x}+3i$ |
| 52000.5-j2 |
52000.5-j |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{8} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.556159794$ |
3.112319589 |
\( -\frac{109815566}{4225} a + \frac{7969262}{4225} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -7 i + 34\) , \( 90 i + 41\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-7i+34\right){x}+90i+41$ |
| 52000.5-k1 |
52000.5-k |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{9} \cdot 5^{9} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.971655697$ |
1.971655697 |
\( -\frac{1374}{65} a + \frac{116018}{65} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -i - 12\) , \( 2 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-i-12\right){x}+2i+1$ |
*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.
