| 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 |
| 2.1-a1 |
2.1-a |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$2.90184$ |
$(-a^2+a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.099363876$ |
$187.8938678$ |
0.967987312 |
\( -\frac{89181}{64} a^{2} + \frac{38961}{64} a + \frac{598617}{64} \) |
\( \bigl[a^{2} - 4\) , \( 0\) , \( a\) , \( 34 a^{2} - 83 a - 10\) , \( 862 a^{2} - 2037 a - 363\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(34a^{2}-83a-10\right){x}+862a^{2}-2037a-363$ |
| 2.1-a2 |
2.1-a |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$2.90184$ |
$(-a^2+a+4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.596183261$ |
$281.8408018$ |
0.967987312 |
\( \frac{1298379874653}{16} a^{2} - \frac{3066083545761}{16} a - \frac{549818786745}{16} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( -2280845779701 a^{2} - 5768071850101 a - 901905802480\) , \( 5676543543244064595 a^{2} + 14355512901873278189 a + 2244653104253838246\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-2280845779701a^{2}-5768071850101a-901905802480\right){x}+5676543543244064595a^{2}+14355512901873278189a+2244653104253838246$ |
| 2.1-a3 |
2.1-a |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$2.90184$ |
$(-a^2+a+4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.298091630$ |
$563.6816036$ |
0.967987312 |
\( \frac{7322067}{4} a^{2} + \frac{21108933}{4} a + \frac{5286861}{4} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a\) , \( -13 a^{2} - 54 a - 48\) , \( 99 a^{2} + 323 a + 212\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-13a^{2}-54a-48\right){x}+99a^{2}+323a+212$ |
| 2.1-a4 |
2.1-a |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$2.90184$ |
$(-a^2+a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.198727753$ |
$93.94693393$ |
0.967987312 |
\( \frac{4279149}{4096} a^{2} - \frac{8096193}{4096} a - \frac{736425}{4096} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a + 1\) , \( 3749943181 a^{2} + 9483298650 a + 1482825165\) , \( -124200434705203 a^{2} - 314092709629754 a - 49112085406711\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(3749943181a^{2}+9483298650a+1482825165\right){x}-124200434705203a^{2}-314092709629754a-49112085406711$ |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$128.9030083$ |
1.113884941 |
\( -\frac{8559329270}{3} a^{2} + \frac{1258291225}{3} a + \frac{51558484228}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a + 1\) , \( -15968862805 a^{2} - 40383943904 a - 6314504093\) , \( 2641776166858284 a^{2} + 6680835187520181 a + 1044627074294126\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15968862805a^{2}-40383943904a-6314504093\right){x}+2641776166858284a^{2}+6680835187520181a+1044627074294126$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$257.8060166$ |
1.113884941 |
\( -20175 a^{2} + \frac{2300}{3} a + \frac{395884}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a + 1\) , \( -3182082735 a^{2} - 8047226169 a - 1258278353\) , \( -201544197089774 a^{2} - 509688739208803 a - 79695822677221\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3182082735a^{2}-8047226169a-1258278353\right){x}-201544197089774a^{2}-509688739208803a-79695822677221$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$64.45150415$ |
1.113884941 |
\( \frac{27913675}{27} a^{2} - 2443238 a - \frac{11784946}{27} \) |
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a^{2} + a - 3\) , \( -634462906071282658909537772459377 a^{2} - 1604504636400832639155322524649954 a - 250883151128430323997501438695096\) , \( -27456497556149171117612926754594310382537194274635 a^{2} - 69435229714154396832682142482005268827100901308353 a - 10857013956089079115351430846034648844863095575132\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-634462906071282658909537772459377a^{2}-1604504636400832639155322524649954a-250883151128430323997501438695096\right){x}-27456497556149171117612926754594310382537194274635a^{2}-69435229714154396832682142482005268827100901308353a-10857013956089079115351430846034648844863095575132$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$128.9030083$ |
1.113884941 |
\( \frac{134}{3} a^{2} + \frac{263}{3} a - \frac{4}{3} \) |
\( \bigl[a\) , \( a^{2} - a - 3\) , \( 1\) , \( a^{2} - 3 a + 2\) , \( a^{2} - 2 a - 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(a^{2}-3a+2\right){x}+a^{2}-2a-1$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$16.11287603$ |
1.113884941 |
\( 20991327338487 a^{2} + \frac{159256034869306}{3} a + \frac{24901554145562}{3} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{2} + a - 3\) , \( -91082584373088213452514 a^{2} - 230340383217881597993465 a - 36016425171236330501674\) , \( -38420432216701411408265125956593751 a^{2} - 97162120959827019655435440394101191 a - 15192439163904967549108955937767120\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-91082584373088213452514a^{2}-230340383217881597993465a-36016425171236330501674\right){x}-38420432216701411408265125956593751a^{2}-97162120959827019655435440394101191a-15192439163904967549108955937767120$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$3.10471$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$128.9030083$ |
1.113884941 |
\( \frac{11356558}{9} a^{2} + \frac{28710361}{9} a + \frac{4505608}{9} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{2} + a - 3\) , \( -5692743642713837386334 a^{2} - 14396481624332341467010 a - 2251059045349335444264\) , \( -600301067580587307025172780888366 a^{2} - 1518112149587523448353112877701615 a - 237374670795108473891536038500755\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-5692743642713837386334a^{2}-14396481624332341467010a-2251059045349335444264\right){x}-600301067580587307025172780888366a^{2}-1518112149587523448353112877701615a-237374670795108473891536038500755$ |
| 3.1-b1 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.439048961$ |
$423.3746465$ |
0.602346440 |
\( \frac{10298}{3} a^{2} + 9738 a + \frac{11473}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} + a - 4\) , \( -29 a^{2} + 64 a + 19\) , \( 1430 a^{2} - 3382 a - 599\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-29a^{2}+64a+19\right){x}+1430a^{2}-3382a-599$ |
| 3.1-b2 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.439048961$ |
$105.8436616$ |
0.602346440 |
\( \frac{7706362858}{3} a^{2} - 6066111270 a - \frac{3263376769}{3} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( 1\) , \( 2826713300976300118 a^{2} + 7148526026961787228 a + 1117756031911981688\) , \( -4164787388931337733138534091 a^{2} - 10532405616181557069773739657 a - 1646865362681500224629672362\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(2826713300976300118a^{2}+7148526026961787228a+1117756031911981688\right){x}-4164787388931337733138534091a^{2}-10532405616181557069773739657a-1646865362681500224629672362$ |
| 3.1-b3 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.512391689$ |
$3.307614426$ |
0.602346440 |
\( \frac{267711895733248}{729} a^{2} + \frac{677021402069782}{729} a + \frac{105860211078073}{729} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 3\) , \( -1573043523 a^{2} - 3978098012 a - 622022361\) , \( -87199054189897 a^{2} - 220519253999915 a - 34480776230161\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1573043523a^{2}-3978098012a-622022361\right){x}-87199054189897a^{2}-220519253999915a-34480776230161$ |
| 3.1-b4 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.756195844$ |
$26.46091541$ |
0.602346440 |
\( -\frac{13567786036}{27} a^{2} + \frac{2284058404}{27} a + \frac{27018336889}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 3\) , \( -98325943 a^{2} - 248658242 a - 38880636\) , \( -1362092552414 a^{2} - 3444620315297 a - 538606856933\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-98325943a^{2}-248658242a-38880636\right){x}-1362092552414a^{2}-3444620315297a-538606856933$ |
| 3.1-b5 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.512391689$ |
$3.307614426$ |
0.602346440 |
\( -\frac{13453678716773991424}{9} a^{2} + \frac{2252807618556982730}{9} a + \frac{80344841487195642215}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 3\) , \( -82505323 a^{2} - 208649192 a - 32624751\) , \( -1815094394147 a^{2} - 4590224807543 a - 717735578933\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-82505323a^{2}-208649192a-32624751\right){x}-1815094394147a^{2}-4590224807543a-717735578933$ |
| 3.1-b6 |
3.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$3.10471$ |
$(a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.878097922$ |
$211.6873232$ |
0.602346440 |
\( \frac{57400}{9} a^{2} - \frac{312152}{9} a + \frac{443641}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 3\) , \( -7144883 a^{2} - 18068822 a - 2825271\) , \( -13886616855 a^{2} - 35118114731 a - 5491129841\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7144883a^{2}-18068822a-2825271\right){x}-13886616855a^{2}-35118114731a-5491129841$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$78.88660978$ |
2.726720123 |
\( \frac{38522917}{2} a^{2} + \frac{97420885}{2} a + 7618039 \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -152118765 a^{2} - 384695878 a - 60151720\) , \( -2622199503003 a^{2} - 6631327410753 a - 1036885951733\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-152118765a^{2}-384695878a-60151720\right){x}-2622199503003a^{2}-6631327410753a-1036885951733$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$157.7732195$ |
2.726720123 |
\( \frac{4339}{4} a^{2} + \frac{11737}{4} a + \frac{4671}{2} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} + a - 4\) , \( 225 a^{2} - 533 a - 93\) , \( -1753 a^{2} + 4139 a + 738\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+{x}^{2}+\left(225a^{2}-533a-93\right){x}-1753a^{2}+4139a+738$ |
| 4.1-b1 |
4.1-b |
$4$ |
$4$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$27.25756807$ |
0.942159380 |
\( -\frac{2698151091885}{2} a^{2} + \frac{451803213819}{2} a + 8056626240519 \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( a + 1\) , \( 125020179757696174021 a^{2} + 316165777613406920298 a + 49436233942303427013\) , \( -797182714701879937164696308010 a^{2} - 2016009682454252160750262953602 a - 315226799826582602675825749937\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(125020179757696174021a^{2}+316165777613406920298a+49436233942303427013\right){x}-797182714701879937164696308010a^{2}-2016009682454252160750262953602a-315226799826582602675825749937$ |
| 4.1-b2 |
4.1-b |
$4$ |
$4$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$6.814392018$ |
0.942159380 |
\( \frac{2277210131137089}{2} a^{2} - \frac{5377560597889119}{2} a - 482159697265593 \) |
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a + 1\) , \( -3742004788 a^{2} - 9463223102 a - 1479686109\) , \( -319687334385757 a^{2} - 808463040647707 a - 126412694988246\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3742004788a^{2}-9463223102a-1479686109\right){x}-319687334385757a^{2}-808463040647707a-126412694988246$ |
| 4.1-b3 |
4.1-b |
$4$ |
$4$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$54.51513614$ |
0.942159380 |
\( \frac{39295683}{4} a^{2} - \frac{96984567}{4} a - \frac{3019293}{2} \) |
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a + 1\) , \( -287272613 a^{2} - 726488867 a - 113595064\) , \( -2543902305904 a^{2} - 6433320223002 a - 1005925201551\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-287272613a^{2}-726488867a-113595064\right){x}-2543902305904a^{2}-6433320223002a-1005925201551$ |
| 4.1-b4 |
4.1-b |
$4$ |
$4$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.25720$ |
$(a^2+3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$109.0302722$ |
0.942159380 |
\( \frac{81099}{16} a^{2} + \frac{295065}{16} a + \frac{43965}{8} \) |
\( \bigl[1\) , \( -a^{2} + a + 5\) , \( 1\) , \( -4 a^{2} + 7 a + 8\) , \( -5 a^{2} + 11 a + 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-4a^{2}+7a+8\right){x}-5a^{2}+11a+4$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.25720$ |
$(-a^2+a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$243.8396390$ |
2.107082724 |
\( -2323 a^{2} + 3802 a + 6989 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( -a^{2} + 16 a - 6\) , \( 18 a^{2} - 25 a - 9\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}+16a-6\right){x}+18a^{2}-25a-9$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.25720$ |
$(-a^2+a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$243.8396390$ |
2.107082724 |
\( 22915602 a^{2} - 54039041 a - 9690983 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( -112 a^{2} - 272 a - 20\) , \( 1388 a^{2} + 3522 a + 578\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-112a^{2}-272a-20\right){x}+1388a^{2}+3522a+578$ |
| 6.1-a1 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$29.77452099$ |
2.058316000 |
\( \frac{42689119200725}{589824} a^{2} + \frac{11995041235775}{65536} a + \frac{16881510079247}{589824} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -8 a^{2} + 18 a\) , \( 17 a^{2} - 41 a - 10\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-8a^{2}+18a\right){x}+17a^{2}-41a-10$ |
| 6.1-a2 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{8} \cdot 3^{3} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$7.443630249$ |
2.058316000 |
\( \frac{53047700433162740905}{768} a^{2} + \frac{134153282191632628115}{768} a + \frac{20976441829098005963}{768} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -143 a^{2} + 318 a + 75\) , \( 1832 a^{2} - 4352 a - 796\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-143a^{2}+318a+75\right){x}+1832a^{2}-4352a-796$ |
| 6.1-a3 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{6} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$119.0980839$ |
2.058316000 |
\( -\frac{51423667517}{144} a^{2} + \frac{956769817}{16} a + \frac{307100350921}{144} \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a^{2} - 3\) , \( 3330138428376116009 a^{2} - 7864017885685354164 a - 1410197956484030179\) , \( -16412163345928071686686970116 a^{2} + 38756811126949010713878407477 a + 6949981122315034880021211301\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3330138428376116009a^{2}-7864017885685354164a-1410197956484030179\right){x}-16412163345928071686686970116a^{2}+38756811126949010713878407477a+6949981122315034880021211301$ |
| 6.1-a4 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{12} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$59.54904199$ |
2.058316000 |
\( -\frac{100914643}{20736} a^{2} + \frac{122426239}{20736} a + \frac{991938967}{20736} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} + a - 4\) , \( -8057999266 a^{2} + 19028713590 a + 3412282787\) , \( -786726324585691 a^{2} + 1857829643045280 a + 333151272568548\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-8057999266a^{2}+19028713590a+3412282787\right){x}-786726324585691a^{2}+1857829643045280a+333151272568548$ |
| 6.1-a5 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{24} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$7.443630249$ |
2.058316000 |
\( \frac{349624110005}{104976} a^{2} - \frac{30578750459}{3888} a - \frac{148053633313}{104976} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} + a - 4\) , \( -123945158391 a^{2} + 292692620255 a + 52486469517\) , \( -55013994083503259 a^{2} + 129913828731324738 a + 23296515656381342\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-123945158391a^{2}+292692620255a+52486469517\right){x}-55013994083503259a^{2}+129913828731324738a+23296515656381342$ |
| 6.1-a6 |
6.1-a |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{32} \cdot 3^{3} \) |
$3.48492$ |
$(-a^2+a+4), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$7.443630249$ |
2.058316000 |
\( -\frac{5355059501094361}{12884901888} a^{2} + \frac{816804592602973}{12884901888} a + \frac{31793709339256741}{12884901888} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( 0\) , \( -17645276782 a^{2} - 44623457315 a - 6977401824\) , \( -3368620655782753 a^{2} - 8518965267721711 a - 1332040308411889\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-17645276782a^{2}-44623457315a-6977401824\right){x}-3368620655782753a^{2}-8518965267721711a-1332040308411889$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$19.95616087$ |
2.069357484 |
\( -\frac{6367977}{8} a^{2} + 1875798 a + 336420 \) |
\( \bigl[a^{2} - 4\) , \( 0\) , \( 1\) , \( -223 a^{2} + 523 a + 101\) , \( -4204 a^{2} + 9926 a + 1782\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-223a^{2}+523a+101\right){x}-4204a^{2}+9926a+1782$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{19} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$59.86848263$ |
2.069357484 |
\( \frac{1167730569}{512} a^{2} - \frac{195354909}{512} a - \frac{3486607209}{256} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a\) , \( 61 a^{2} + 125 a - 42\) , \( -57 a^{2} - 83 a + 120\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(61a^{2}+125a-42\right){x}-57a^{2}-83a+120$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{46} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$12.78166036$ |
3.092591687 |
\( -\frac{258789938169603}{268435456} a^{2} - \frac{526182438551441}{268435456} a + \frac{2985751172286727}{268435456} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 2725572727 a^{2} + 6892749812 a + 1077762416\) , \( 1601315007267175 a^{2} + 4049594277162910 a + 633201643670714\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2725572727a^{2}+6892749812a+1077762416\right){x}+1601315007267175a^{2}+4049594277162910a+633201643670714$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{50} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$12.78166036$ |
3.092591687 |
\( \frac{157794365}{262144} a^{2} + \frac{600984689}{131072} a + \frac{1293651173}{262144} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( -87 a^{2} + 206 a + 34\) , \( -1438 a^{2} + 3387 a + 630\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-87a^{2}+206a+34\right){x}-1438a^{2}+3387a+630$ |
| 8.1-c1 |
8.1-c |
$2$ |
$5$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$91.58626381$ |
0.633136876 |
\( \frac{10703}{32} a^{2} - \frac{13079}{32} a - \frac{35323}{32} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 1\) , \( -3 a^{2} - 9 a - 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(a^{2}-a-1\right){x}-3a^{2}-9a-1$ |
| 8.1-c2 |
8.1-c |
$2$ |
$5$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{31} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.732690110$ |
0.633136876 |
\( -\frac{147991960572087}{8192} a^{2} - \frac{1496950335049241}{32768} a - \frac{234064807591457}{32768} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( -1398800 a^{2} + 3303216 a + 592359\) , \( -2085023605 a^{2} + 4923718113 a + 882935093\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-1398800a^{2}+3303216a+592359\right){x}-2085023605a^{2}+4923718113a+882935093$ |
| 8.1-d1 |
8.1-d |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{54} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$3.425568414$ |
0.710429794 |
\( \frac{58614720967075865277}{281474976710656} a^{2} - \frac{5621742393782241361}{281474976710656} a - \frac{339380984228329467321}{281474976710656} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( -5674350082 a^{2} - 14349965815 a - 2243785744\) , \( -590545689569442 a^{2} - 1493441598954940 a - 233517140350901\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-5674350082a^{2}-14349965815a-2243785744\right){x}-590545689569442a^{2}-1493441598954940a-233517140350901$ |
| 8.1-d2 |
8.1-d |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$92.49034719$ |
0.710429794 |
\( \frac{38603026758429}{65536} a^{2} - \frac{91158895488561}{65536} a - \frac{16346875618969}{65536} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( -559192197 a^{2} - 1414151185 a - 221119144\) , \( 18069331097057 a^{2} + 45695855887649 a + 7145083945868\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-559192197a^{2}-1414151185a-221119144\right){x}+18069331097057a^{2}+45695855887649a+7145083945868$ |
| 8.1-d3 |
8.1-d |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{36} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.851136828$ |
0.710429794 |
\( -\frac{4065319953198902053}{16777216} a^{2} + \frac{680734541197776729}{16777216} a + \frac{24277931297534163969}{16777216} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( 1263 a^{2} - 231 a - 7488\) , \( 39957 a^{2} - 6770 a - 238419\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(1263a^{2}-231a-7488\right){x}+39957a^{2}-6770a-238419$ |
| 8.1-d4 |
8.1-d |
$4$ |
$6$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$3.65608$ |
$(-a^2+a+4), (a^2+3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$184.9806943$ |
0.710429794 |
\( \frac{28472307435}{256} a^{2} + \frac{72014723529}{256} a + \frac{11263547057}{256} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( 13 a^{2} + 4 a - 88\) , \( 37 a^{2} - 12 a - 204\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(13a^{2}+4a-88\right){x}+37a^{2}-12a-204$ |
| 9.1-a1 |
9.1-a |
$2$ |
$3$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$3.72856$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.211368464$ |
$49.62331419$ |
2.175276562 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} + a - 5\) , \( a^{2} - 4\) , \( -a^{2} + a + 9\) , \( -91479584 a^{2} + 216026184 a + 38738418\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-a^{2}+a+9\right){x}-91479584a^{2}+216026184a+38738418$ |
| 9.1-a2 |
9.1-a |
$2$ |
$3$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.72856$ |
$(a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.634105394$ |
$148.8699425$ |
2.175276562 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a^{2} - 4\) , \( 0\) , \( 17 a^{2} - 40 a - 9\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+17a^{2}-40a-9$ |
| 9.1-b1 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$81.37667952$ |
1.406394762 |
\( 20991327338487 a^{2} + \frac{159256034869306}{3} a + \frac{24901554145562}{3} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} + a - 4\) , \( -1948498342485313329355 a^{2} - 4927592448069408237643 a - 770486973238931154508\) , \( 120215174200602131401472903306803 a^{2} + 304014312775172597411578987836572 a + 47536209648025877145801914794726\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-1948498342485313329355a^{2}-4927592448069408237643a-770486973238931154508\right){x}+120215174200602131401472903306803a^{2}+304014312775172597411578987836572a+47536209648025877145801914794726$ |
| 9.1-b2 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$162.7533590$ |
1.406394762 |
\( \frac{11356558}{9} a^{2} + \frac{28710361}{9} a + \frac{4505608}{9} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} + a - 4\) , \( -121782903157270451725 a^{2} - 307978970685861466993 a - 48156130492886183293\) , \( 1878305194540594666651058997382 a^{2} + 4750079735752989391484723231741 a + 742730775082223495005156516243\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-121782903157270451725a^{2}-307978970685861466993a-48156130492886183293\right){x}+1878305194540594666651058997382a^{2}+4750079735752989391484723231741a+742730775082223495005156516243$ |
| 9.1-b3 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$40.68833976$ |
1.406394762 |
\( -\frac{8559329270}{3} a^{2} + \frac{1258291225}{3} a + \frac{51558484228}{3} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 4\) , \( -341616381 a^{2} - 863919797 a - 135084003\) , \( -8266231732442 a^{2} - 20904621867329 a - 3268683236085\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-341616381a^{2}-863919797a-135084003\right){x}-8266231732442a^{2}-20904621867329a-3268683236085$ |
| 9.1-b4 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$162.7533590$ |
1.406394762 |
\( -20175 a^{2} + \frac{2300}{3} a + \frac{395884}{3} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 4\) , \( -68073201 a^{2} - 172151537 a - 26917908\) , \( 630564373231 a^{2} + 1594645566694 a + 249341569746\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-68073201a^{2}-172151537a-26917908\right){x}+630564373231a^{2}+1594645566694a+249341569746$ |
| 9.1-b5 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$81.37667952$ |
1.406394762 |
\( \frac{134}{3} a^{2} + \frac{263}{3} a - \frac{4}{3} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 5 a^{2} - 15 a + 3\) , \( 117 a^{2} - 278 a - 54\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(5a^{2}-15a+3\right){x}+117a^{2}-278a-54$ |
| 9.1-b6 |
9.1-b |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$40.68833976$ |
1.406394762 |
\( \frac{27913675}{27} a^{2} - 2443238 a - \frac{11784946}{27} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( 1\) , \( -13572846327948275073507290535007 a^{2} - 34324614810345230377266084237762 a - 5367056803404405154393328657809\) , \( 85909695603580751950109787974714617030634452014 a^{2} + 217258571917587844047979979083871977278522384067 a + 33970930277031921133794673495373430857628179610\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-13572846327948275073507290535007a^{2}-34324614810345230377266084237762a-5367056803404405154393328657809\right){x}+85909695603580751950109787974714617030634452014a^{2}+217258571917587844047979979083871977278522384067a+33970930277031921133794673495373430857628179610$ |
| 9.1-c1 |
9.1-c |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.22039803$ |
1.113699878 |
\( \frac{267711895733248}{729} a^{2} + \frac{677021402069782}{729} a + \frac{105860211078073}{729} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 3\) , \( 0\) , \( -30935266121978 a^{2} - 78232750009546 a - 12232609615788\) , \( 240486113087132652352 a^{2} + 608169649865972379366 a + 95094470104686151863\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-30935266121978a^{2}-78232750009546a-12232609615788\right){x}+240486113087132652352a^{2}+608169649865972379366a+95094470104686151863$ |
| 9.1-c2 |
9.1-c |
$6$ |
$8$ |
3.3.837.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$3.72856$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$128.8815921$ |
1.113699878 |
\( -\frac{13567786036}{27} a^{2} + \frac{2284058404}{27} a + \frac{27018336889}{9} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 3\) , \( 0\) , \( -1933665002973 a^{2} - 4890080149406 a - 764621484598\) , \( 3756734613917348220 a^{2} + 9500473625924882948 a + 1485510671898823784\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-1933665002973a^{2}-4890080149406a-764621484598\right){x}+3756734613917348220a^{2}+9500473625924882948a+1485510671898823784$ |
*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.
