| 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 |
| 2.2-a1 |
2.2-a |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{7} \) |
$4.22223$ |
$(-a^2+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.079484284$ |
$238.4274907$ |
1.350600768 |
\( \frac{34442819}{128} a^{2} + \frac{2974079}{32} a - \frac{63551943}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 17 a^{2} - 7 a - 203\) , \( -\frac{175}{2} a^{2} + \frac{59}{2} a + 1068\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a^{2}-7a-203\right){x}-\frac{175}{2}a^{2}+\frac{59}{2}a+1068$ |
| 2.2-b1 |
2.2-b |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{2} \) |
$4.22223$ |
$(-a^2+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.017415162$ |
$254.1239115$ |
0.630801116 |
\( -\frac{493}{4} a^{2} - 65 a + 1010 \) |
\( \bigl[a\) , \( -1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -534 a^{2} + 183 a + 6526\) , \( 15671 a^{2} - 5418 a - 191600\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}-{x}^{2}+\left(-534a^{2}+183a+6526\right){x}+15671a^{2}-5418a-191600$ |
| 4.2-a1 |
4.2-a |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$4.73930$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$20.77491556$ |
1.974092051 |
\( -\frac{140977}{32} a^{2} - \frac{39761}{4} a + \frac{18783}{2} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( a + 1\) , \( -90 a^{2} + 30 a + 1103\) , \( \frac{1737}{2} a^{2} - \frac{601}{2} a - 10623\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-90a^{2}+30a+1103\right){x}+\frac{1737}{2}a^{2}-\frac{601}{2}a-10623$ |
| 4.2-b1 |
4.2-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$4.73930$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$4.074489725$ |
$2.951913263$ |
1.714337049 |
\( \frac{402747998693}{8192} a^{2} - \frac{139210871535}{8192} a - \frac{2462045332401}{4096} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 9 a^{2} + a - 127\) , \( \frac{139}{2} a^{2} - \frac{31}{2} a - 882\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(9a^{2}+a-127\right){x}+\frac{139}{2}a^{2}-\frac{31}{2}a-882$ |
| 4.2-b2 |
4.2-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$4.73930$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.358163241$ |
$79.70165811$ |
1.714337049 |
\( \frac{2571}{32} a^{2} - \frac{7897}{32} a - \frac{2779}{16} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -a^{2} + a + 8\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-a^{2}+a+8\right){x}-\frac{1}{2}a^{2}+\frac{1}{2}a+4$ |
| 4.2-c1 |
4.2-c |
$2$ |
$2$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{27} \) |
$4.73930$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$37.30223180$ |
2.215353146 |
\( -\frac{1277290809835}{131072} a^{2} + \frac{110371301385}{32768} a + \frac{1952063422079}{16384} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 208766 a^{2} - 903547 a + 501836\) , \( \frac{48529527}{2} a^{2} - \frac{210037315}{2} a + 58328209\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(208766a^{2}-903547a+501836\right){x}+\frac{48529527}{2}a^{2}-\frac{210037315}{2}a+58328209$ |
| 4.2-c2 |
4.2-c |
$2$ |
$2$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{39} \) |
$4.73930$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$37.30223180$ |
2.215353146 |
\( \frac{32653882287117}{17179869184} a^{2} + \frac{9043493086945}{4294967296} a - \frac{26393265290137}{2147483648} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 0\) , \( -\frac{35}{2} a^{2} - \frac{99}{2} a + 29\) , \( -171 a^{2} - 448 a + 403\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(-\frac{35}{2}a^{2}-\frac{99}{2}a+29\right){x}-171a^{2}-448a+403$ |
| 4.3-a1 |
4.3-a |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.73930$ |
$(-a^2+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$37.36582845$ |
2.662956128 |
\( 15916016 a^{2} - 5507392 a - 194609536 \) |
\( \bigl[0\) , \( a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{218136117177887593881}{2} a^{2} - \frac{944099940514978148513}{2} a + 262180368155069763502\) , \( 114494837540539759951776540335 a^{2} - 495537239361172580150717219946 a + 275225387217780406432400596795\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+a{x}^{2}+\left(\frac{218136117177887593881}{2}a^{2}-\frac{944099940514978148513}{2}a+262180368155069763502\right){x}+114494837540539759951776540335a^{2}-495537239361172580150717219946a+275225387217780406432400596795$ |
| 4.3-a2 |
4.3-a |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.73930$ |
$(-a^2+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$112.0974853$ |
2.662956128 |
\( -400 a^{2} + 2240 a - 1408 \) |
\( \bigl[0\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{8299}{2} a^{2} + \frac{35915}{2} a - 9966\) , \( 586532 a^{2} - 2538532 a + 1409924\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-\frac{8299}{2}a^{2}+\frac{35915}{2}a-9966\right){x}+586532a^{2}-2538532a+1409924$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$50.04860390$ |
2.972351165 |
\( -\frac{4218035}{2592} a^{2} + \frac{655585}{648} a + \frac{6471499}{324} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{197}{2} a^{2} - \frac{77}{2} a - 1188\) , \( 1147 a^{2} - 403 a - 14001\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(\frac{197}{2}a^{2}-\frac{77}{2}a-1188\right){x}+1147a^{2}-403a-14001$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$100.0972078$ |
2.972351165 |
\( \frac{42159253015}{3145728} a^{2} + \frac{27743716435}{786432} a - \frac{11056109819}{393216} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{87945357498166302255703298501}{2} a^{2} + \frac{380630259017941043250537609101}{2} a - 105702560881265214860230120264\) , \( -\frac{23919569761128204228722535739181799130958527}{2} a^{2} + \frac{103524646357435882319393045728622278662308595}{2} a - 28749212588987904521946382046045963420763509\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+{x}^{2}+\left(-\frac{87945357498166302255703298501}{2}a^{2}+\frac{380630259017941043250537609101}{2}a-105702560881265214860230120264\right){x}-\frac{23919569761128204228722535739181799130958527}{2}a^{2}+\frac{103524646357435882319393045728622278662308595}{2}a-28749212588987904521946382046045963420763509$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3 \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 5 \) |
$1$ |
$25.02430195$ |
2.972351165 |
\( \frac{63338053632025}{96} a^{2} - \frac{68532338687975}{24} a + \frac{19031818773511}{12} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 1\) , \( -64539309339128 a^{2} + 279328150222179 a - 155141111906801\) , \( -1053799031736343144007 a^{2} + 4560875182195069605071 a - 2533146932993061251487\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-64539309339128a^{2}+279328150222179a-155141111906801\right){x}-1053799031736343144007a^{2}+4560875182195069605071a-2533146932993061251487$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$100.0972078$ |
2.972351165 |
\( \frac{1415718725}{9216} a^{2} - \frac{1533408775}{2304} a + \frac{430303631}{1152} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 1\) , \( -\frac{8067865082641}{2} a^{2} + \frac{34917972517093}{2} a - 9696862055466\) , \( -\frac{32927359251777361949}{2} a^{2} + \frac{142510641122155153057}{2} a - 39575780859641829907\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-\frac{8067865082641}{2}a^{2}+\frac{34917972517093}{2}a-9696862055466\right){x}-\frac{32927359251777361949}{2}a^{2}+\frac{142510641122155153057}{2}a-39575780859641829907$ |
| 6.1-b1 |
6.1-b |
$2$ |
$2$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{14} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.52490194$ |
1.290818114 |
\( -\frac{4197921406643}{612220032} a^{2} + \frac{2362251601441}{153055008} a + \frac{2744131944535}{76527504} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( 1\) , \( -49691112 a^{2} + 215064682 a - 119448646\) , \( -718647989882 a^{2} + 3110330986339 a - 1727502964639\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-49691112a^{2}+215064682a-119448646\right){x}-718647989882a^{2}+3110330986339a-1727502964639$ |
| 6.1-b2 |
6.1-b |
$2$ |
$2$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{14} \cdot 3^{7} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$15.52490194$ |
1.290818114 |
\( \frac{10922686239313999}{35831808} a^{2} - \frac{11818363535495573}{8957952} a + \frac{3282003923616685}{4478976} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -4 a^{2} + 13 a + 8\) , \( -\frac{9}{2} a^{2} + \frac{51}{2} a - 37\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-4a^{2}+13a+8\right){x}-\frac{9}{2}a^{2}+\frac{51}{2}a-37$ |
| 6.1-c1 |
6.1-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{4} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.079957123$ |
$47.80129543$ |
1.089547622 |
\( -\frac{8183741}{5184} a^{2} - \frac{5977937}{1296} a + \frac{1879177}{648} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a + 1\) , \( -\frac{86849}{2} a^{2} - \frac{232213}{2} a + 94567\) , \( -\frac{32955597}{2} a^{2} - \frac{88113313}{2} a + 35882753\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{86849}{2}a^{2}-\frac{232213}{2}a+94567\right){x}-\frac{32955597}{2}a^{2}-\frac{88113313}{2}a+35882753$ |
| 6.1-c2 |
6.1-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{12} \) |
$5.07063$ |
$(-a^2+11), (1/2a^2-1/2a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.239871371$ |
$15.93376514$ |
1.089547622 |
\( -\frac{10902468125}{2125764} a^{2} + \frac{11948797135}{531441} a - \frac{6334586158}{531441} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -\frac{1}{2} a^{2} - \frac{5}{2} a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}-\frac{1}{2}a^{2}-\frac{5}{2}a+1$ |
| 6.2-a1 |
6.2-a |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{23} \cdot 3 \) |
$5.07063$ |
$(-1/2a^2-1/2a+4), (1/2a^2-1/2a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$51.65807172$ |
1.227174527 |
\( \frac{1098382103}{24576} a^{2} - \frac{4763678791}{24576} a + \frac{671926765}{6144} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -3 a^{2} + 43 a - 29\) , \( \frac{59}{2} a^{2} - \frac{373}{2} a + 107\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+{x}^{2}+\left(-3a^{2}+43a-29\right){x}+\frac{59}{2}a^{2}-\frac{373}{2}a+107$ |
| 6.2-b1 |
6.2-b |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{11} \cdot 3 \) |
$5.07063$ |
$(-1/2a^2-1/2a+4), (1/2a^2-1/2a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$100.8727297$ |
2.396304012 |
\( \frac{139799}{384} a^{2} - \frac{631399}{384} a + \frac{89941}{96} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{35}{2} a^{2} + \frac{9}{2} a + 207\) , \( -929 a^{2} + 314 a + 11330\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-\frac{35}{2}a^{2}+\frac{9}{2}a+207\right){x}-929a^{2}+314a+11330$ |
| 6.2-c1 |
6.2-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{15} \) |
$5.07063$ |
$(-1/2a^2-1/2a+4), (1/2a^2-1/2a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$13.11956221$ |
0.934993817 |
\( \frac{917381936400773}{114791256} a^{2} - \frac{3970480239991045}{114791256} a + \frac{551309759590195}{28697814} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -59 a^{2} + 250 a - 141\) , \( -1003 a^{2} + 4304 a - 2389\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a^{2}+250a-141\right){x}-1003a^{2}+4304a-2389$ |
| 6.2-c2 |
6.2-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{5} \) |
$5.07063$ |
$(-1/2a^2-1/2a+4), (1/2a^2-1/2a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$39.35868664$ |
0.934993817 |
\( -\frac{75504078845}{972} a^{2} - \frac{204810367295}{972} a + \frac{38663467616}{243} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( a\) , \( -\frac{806113}{2} a^{2} - \frac{2155303}{2} a + 877727\) , \( -\frac{908546579}{2} a^{2} - \frac{2429178963}{2} a + 989244775\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-\frac{806113}{2}a^{2}-\frac{2155303}{2}a+877727\right){x}-\frac{908546579}{2}a^{2}-\frac{2429178963}{2}a+989244775$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$95.73956276$ |
1.137180974 |
\( -\frac{199107}{16} a^{2} + \frac{16649}{4} a + \frac{305311}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( 0\) , \( \frac{231535338342491187}{2} a^{2} - \frac{1002092188970254291}{2} a + 278285049871129418\) , \( 70424461263125596635881093 a^{2} - 304799271892679054034152722 a + 169287978716808300989830669\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(\frac{231535338342491187}{2}a^{2}-\frac{1002092188970254291}{2}a+278285049871129418\right){x}+70424461263125596635881093a^{2}-304799271892679054034152722a+169287978716808300989830669$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$191.4791255$ |
1.137180974 |
\( \frac{560283649}{2} a^{2} + 749150204 a - 609565944 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( a\) , \( -\frac{57}{2} a^{2} + \frac{229}{2} a - 44\) , \( -282 a^{2} + 1215 a - 661\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{57}{2}a^{2}+\frac{229}{2}a-44\right){x}-282a^{2}+1215a-661$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$382.9582510$ |
1.137180974 |
\( \frac{14525}{4} a^{2} + 9425 a - 5922 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( a\) , \( -6 a^{2} + 17 a + 11\) , \( \frac{15}{2} a^{2} - \frac{77}{2} a + 37\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-6a^{2}+17a+11\right){x}+\frac{15}{2}a^{2}-\frac{77}{2}a+37$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$191.4791255$ |
1.137180974 |
\( \frac{312355}{2} a^{2} - 675810 a + 376996 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -228230 a^{2} + 987792 a - 548628\) , \( 221605117 a^{2} - 959113876 a + 532699597\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-228230a^{2}+987792a-548628\right){x}+221605117a^{2}-959113876a+532699597$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.125728350$ |
$140.8953391$ |
3.787394086 |
\( -\frac{861}{8} a^{2} + \frac{323}{2} a + 1301 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( a - 1\) , \( 0\) , \( 16 a^{2} + 42 a - 32\) , \( 216 a^{2} + 578 a - 470\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a^{2}+42a-32\right){x}+216a^{2}+578a-470$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{17} \) |
$5.31968$ |
$(-1/2a^2-1/2a+4), (-a^2+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.041909450$ |
$46.96511305$ |
3.787394086 |
\( -\frac{7309837}{512} a^{2} - \frac{5003745}{128} a + \frac{1817241}{64} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( \frac{7019}{2} a^{2} - \frac{30393}{2} a + 8464\) , \( -821741 a^{2} + 3556515 a - 1975297\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(\frac{7019}{2}a^{2}-\frac{30393}{2}a+8464\right){x}-821741a^{2}+3556515a-1975297$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$5.52125$ |
$(-1/2a^2-1/2a+4), (3/2a^2+1/2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.209660631$ |
$75.46835670$ |
1.127641836 |
\( \frac{4301}{40} a^{2} - \frac{2493}{40} a + \frac{311}{10} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -\frac{631}{2} a^{2} + \frac{219}{2} a + 3855\) , \( 51022 a^{2} - 17636 a - 623805\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-\frac{631}{2}a^{2}+\frac{219}{2}a+3855\right){x}+51022a^{2}-17636a-623805$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{3} \) |
$5.52125$ |
$(-1/2a^2-1/2a+4), (3/2a^2+1/2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.628981895$ |
$25.15611890$ |
1.127641836 |
\( \frac{96251907}{500} a^{2} - \frac{30749231}{500} a - \frac{296852148}{125} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{16257650429}{2} a^{2} + \frac{70363619741}{2} a - 19540261501\) , \( -1523047015159288 a^{2} + 6591795136982291 a - 3661136287910607\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{16257650429}{2}a^{2}+\frac{70363619741}{2}a-19540261501\right){x}-1523047015159288a^{2}+6591795136982291a-3661136287910607$ |
| 10.2-a1 |
10.2-a |
$4$ |
$6$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{6} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$86.02220513$ |
3.065278729 |
\( \frac{11263932527}{125000} a^{2} + \frac{7547964171}{31250} a - \frac{3034911539}{15625} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( a - 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{1524502058340516607}{2} a^{2} + \frac{6598092609398216521}{2} a - 1832316977490398023\) , \( -15048270256908873712721887739 a^{2} + 65129384524687734809503240972 a - 36173386480845411037820080945\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1524502058340516607}{2}a^{2}+\frac{6598092609398216521}{2}a-1832316977490398023\right){x}-15048270256908873712721887739a^{2}+65129384524687734809503240972a-36173386480845411037820080945$ |
| 10.2-a2 |
10.2-a |
$4$ |
$6$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$86.02220513$ |
3.065278729 |
\( \frac{36009201}{8000} a^{2} - \frac{40285227}{2000} a + \frac{12481043}{1000} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( a - 1\) , \( a + 1\) , \( -\frac{1112150692212515}{2} a^{2} + \frac{4813422994529969}{2} a - 1336707014411595\) , \( -\frac{52945827666159173496125}{2} a^{2} + \frac{229151198787379187849343}{2} a - 63636213797958076205355\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1112150692212515}{2}a^{2}+\frac{4813422994529969}{2}a-1336707014411595\right){x}-\frac{52945827666159173496125}{2}a^{2}+\frac{229151198787379187849343}{2}a-63636213797958076205355$ |
| 10.2-a3 |
10.2-a |
$4$ |
$6$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{2} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$258.0666153$ |
3.065278729 |
\( -\frac{44419497}{50} a^{2} + \frac{7692838}{25} a + \frac{271592916}{25} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{37}{2} a^{2} - \frac{165}{2} a + 57\) , \( 1751 a^{2} - 7580 a + 4220\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(\frac{37}{2}a^{2}-\frac{165}{2}a+57\right){x}+1751a^{2}-7580a+4220$ |
| 10.2-a4 |
10.2-a |
$4$ |
$6$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$258.0666153$ |
3.065278729 |
\( \frac{22281}{20} a^{2} - \frac{18867}{5} a - \frac{2954}{5} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( a + 1\) , \( -\frac{1}{2} a^{2} - \frac{3}{2} a + 19\) , \( -a^{2} + 4 a + 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{1}{2}a^{2}-\frac{3}{2}a+19\right){x}-a^{2}+4a+8$ |
| 10.2-b1 |
10.2-b |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{10} \cdot 5^{6} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.651850563$ |
$38.98021104$ |
2.536218045 |
\( \frac{65929815341}{16000000} a^{2} + \frac{57255524993}{4000000} a + \frac{20893653063}{2000000} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( a + 1\) , \( -384 a^{2} + 1661 a - 917\) , \( -13772 a^{2} + 59605 a - 33105\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-384a^{2}+1661a-917\right){x}-13772a^{2}+59605a-33105$ |
| 10.2-b2 |
10.2-b |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{12} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.303701126$ |
$9.745052760$ |
2.536218045 |
\( \frac{5136677927496602983}{7812500000} a^{2} + \frac{3433482770328364059}{1953125000} a - \frac{1398227954122525031}{976562500} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( a + 1\) , \( 546 a^{2} - 2364 a + 1318\) , \( -\frac{138537}{2} a^{2} + \frac{599591}{2} a - 166509\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(546a^{2}-2364a+1318\right){x}-\frac{138537}{2}a^{2}+\frac{599591}{2}a-166509$ |
| 10.2-b3 |
10.2-b |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{5} \cdot 5^{3} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.825925281$ |
$77.96042208$ |
2.536218045 |
\( -\frac{144248893947}{4000} a^{2} + \frac{12464686169}{1000} a + \frac{220454070979}{500} \) |
\( \bigl[1\) , \( -a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{46871418047}{2} a^{2} + \frac{202860963889}{2} a - 56335309338\) , \( 6407040464610606 a^{2} - 27729871603899189 a + 15401394776145017\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-\frac{46871418047}{2}a^{2}+\frac{202860963889}{2}a-56335309338\right){x}+6407040464610606a^{2}-27729871603899189a+15401394776145017$ |
| 10.2-b4 |
10.2-b |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{20} \cdot 5^{3} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.303701126$ |
$9.745052760$ |
2.536218045 |
\( \frac{277178270836921}{131072000} a^{2} - \frac{299909405593667}{32768000} a + \frac{83286426225003}{16384000} \) |
\( \bigl[1\) , \( -a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -21 a^{2} - 5 a + 223\) , \( \frac{1387}{2} a^{2} - \frac{1451}{2} a - 10092\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-21a^{2}-5a+223\right){x}+\frac{1387}{2}a^{2}-\frac{1451}{2}a-10092$ |
| 10.2-c1 |
10.2-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{21} \cdot 5 \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$0.076034368$ |
$32.42405874$ |
3.689657136 |
\( -\frac{27140550677}{10485760} a^{2} + \frac{23134942199}{2621440} a - \frac{5045400191}{1310720} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 1\) , \( -83 a^{2} + 27 a + 1027\) , \( -\frac{1989}{2} a^{2} + \frac{685}{2} a + 12167\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-83a^{2}+27a+1027\right){x}-\frac{1989}{2}a^{2}+\frac{685}{2}a+12167$ |
| 10.2-c2 |
10.2-c |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{3} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$0.025344789$ |
$97.27217622$ |
3.689657136 |
\( \frac{173835227}{16000} a^{2} - \frac{14768729}{4000} a - \frac{262859439}{2000} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 1850 a^{2} + 4624 a - 5095\) , \( -\frac{58547}{2} a^{2} - \frac{147891}{2} a + 78136\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(1850a^{2}+4624a-5095\right){x}-\frac{58547}{2}a^{2}-\frac{147891}{2}a+78136$ |
| 10.2-d1 |
10.2-d |
$1$ |
$1$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{13} \cdot 5^{3} \) |
$5.52125$ |
$(-a^2+11), (3/2a^2+1/2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.112535469$ |
$82.94955902$ |
0.665262285 |
\( -\frac{8772257591782477}{1024000} a^{2} - \frac{5863591423039521}{256000} a + \frac{2387854994985689}{128000} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( a + 1\) , \( \frac{111}{2} a^{2} - \frac{495}{2} a + 146\) , \( 3907 a^{2} - 16909 a + 9386\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(\frac{111}{2}a^{2}-\frac{495}{2}a+146\right){x}+3907a^{2}-16909a+9386$ |
| 12.1-a1 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{23} \cdot 3^{8} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$6.860100500$ |
1.140766238 |
\( -\frac{377495989315}{1679616} a^{2} - \frac{63988468435}{419904} a + \frac{3329112451561}{1679616} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( -27352624185062495932 a^{2} + 118383013322764820589 a - 65750882262186936487\) , \( 1392975821715057435249955775997 a^{2} - 6028842941893625834049043912041 a + 3348468089496056399863050505083\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-27352624185062495932a^{2}+118383013322764820589a-65750882262186936487\right){x}+1392975821715057435249955775997a^{2}-6028842941893625834049043912041a+3348468089496056399863050505083$ |
| 12.1-a2 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$27.44040200$ |
1.140766238 |
\( \frac{8824959845828607410450665}{49152} a^{2} - \frac{9548675585335878020658515}{12288} a + \frac{2651705791879764753775099}{6144} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( -\frac{6608163}{2} a^{2} + \frac{28600371}{2} a - 7942496\) , \( 12204266047 a^{2} - 52820445344 a + 29336902272\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{6608163}{2}a^{2}+\frac{28600371}{2}a-7942496\right){x}+12204266047a^{2}-52820445344a+29336902272$ |
| 12.1-a3 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{32} \cdot 3^{2} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 7 \) |
$1$ |
$27.44040200$ |
1.140766238 |
\( \frac{6130659699417990725}{2415919104} a^{2} - \frac{6633110964424167175}{603979776} a + \frac{1842044115244577039}{301989888} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( -\frac{413013}{2} a^{2} + \frac{1787521}{2} a - 496386\) , \( 190577452 a^{2} - 824825179 a + 458114578\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{413013}{2}a^{2}+\frac{1787521}{2}a-496386\right){x}+190577452a^{2}-824825179a+458114578$ |
| 12.1-a4 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{11} \cdot 3^{2} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.715025125$ |
1.140766238 |
\( \frac{367735129431146387283667355}{1152} a^{2} + \frac{245803150036223596041316295}{288} a - \frac{100099450524395989546983451}{144} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( -\frac{9507283266755}{2} a^{2} + \frac{41147819456611}{2} a - 11426915722527\) , \( -478685508280045938 a^{2} + 2071765857664148328 a - 1150675499454441021\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{9507283266755}{2}a^{2}+\frac{41147819456611}{2}a-11426915722527\right){x}-478685508280045938a^{2}+2071765857664148328a-1150675499454441021$ |
| 12.1-a5 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$13.72020100$ |
1.140766238 |
\( \frac{163074443293340525}{1327104} a^{2} + \frac{109002922321983425}{331776} a - \frac{44389719866202361}{165888} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( -\frac{6457951831275}{2} a^{2} + \frac{27950217591811}{2} a - 7761888359227\) , \( 11754590316971341582 a^{2} - 50874234687054077012 a + 28255961064002730543\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{6457951831275}{2}a^{2}+\frac{27950217591811}{2}a-7761888359227\right){x}+11754590316971341582a^{2}-50874234687054077012a+28255961064002730543$ |
| 12.1-a6 |
12.1-a |
$6$ |
$8$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{58} \cdot 3 \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 7 \) |
$1$ |
$6.860100500$ |
1.140766238 |
\( -\frac{2063281007773628970985}{216172782113783808} a^{2} + \frac{2220535164484941246035}{54043195528445952} a - \frac{616060864319188464379}{27021597764222976} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( 11 a^{2} - 36 a - 224\) , \( -42480 a^{2} + 14351 a + 518246\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(11a^{2}-36a-224\right){x}-42480a^{2}+14351a+518246$ |
| 12.1-b1 |
12.1-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{6} \cdot 3^{9} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$19.30184210$ |
0.458529096 |
\( \frac{3154863049}{629856} a^{2} - \frac{298770785}{157464} a - \frac{4739733893}{78732} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 31207133102 a^{2} - 135065448525 a + 75016441603\) , \( 3289820353282479 a^{2} - 14238445425826074 a + 7908147651535061\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(31207133102a^{2}-135065448525a+75016441603\right){x}+3289820353282479a^{2}-14238445425826074a+7908147651535061$ |
| 12.1-b2 |
12.1-b |
$2$ |
$3$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{18} \cdot 3^{3} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$0.714883041$ |
0.458529096 |
\( \frac{15923840169149192521}{884736} a^{2} - \frac{1376084506928734067}{221184} a - \frac{24335969368189499621}{110592} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( a\) , \( -\frac{193}{2} a^{2} - \frac{493}{2} a + 224\) , \( -1768 a^{2} - 4706 a + 3850\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{193}{2}a^{2}-\frac{493}{2}a+224\right){x}-1768a^{2}-4706a+3850$ |
| 12.1-c1 |
12.1-c |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{3} \cdot 3^{4} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$13.96629524$ |
1.327117424 |
\( \frac{233167677658947919}{162} a^{2} - \frac{2018314009214057929}{324} a + \frac{280246977719279311}{81} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( 0\) , \( -\frac{2099310357}{2} a^{2} + \frac{9085880911}{2} a - 2523185839\) , \( -\frac{138243690615501}{2} a^{2} + \frac{598323018559239}{2} a - 166156719802299\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(-\frac{2099310357}{2}a^{2}+\frac{9085880911}{2}a-2523185839\right){x}-\frac{138243690615501}{2}a^{2}+\frac{598323018559239}{2}a-166156719802299$ |
| 12.1-c2 |
12.1-c |
$4$ |
$4$ |
3.3.1772.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$5.69159$ |
$(-1/2a^2-1/2a+4), (-a^2+11), (1/2a^2-1/2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$111.7303619$ |
1.327117424 |
\( \frac{1031043617}{144} a^{2} - \frac{559545887}{18} a + \frac{158172997}{9} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( 0\) , \( -65603526 a^{2} + 283934113 a - 157699299\) , \( -1080205606562 a^{2} + 4675163664289 a - 2596623679523\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(-65603526a^{2}+283934113a-157699299\right){x}-1080205606562a^{2}+4675163664289a-2596623679523$ |
*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.
