| 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 |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.58863$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$16.93299769$ |
1.593706155 |
\( 21224 a^{2} - 15060 a - 133604 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( a\) , \( -4 a^{2} + 2 a + 25\) , \( -4 a^{2} + 3 a + 22\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-4a^{2}+2a+25\right){x}-4a^{2}+3a+22$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.58863$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$132.5657523$ |
4.158957543 |
\( 21224 a^{2} - 15060 a - 133604 \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 4\) , \( -561 a^{2} - 1041 a + 392\) , \( -22922 a^{2} - 42538 a + 16053\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-561a^{2}-1041a+392\right){x}-22922a^{2}-42538a+16053$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$182.2020972$ |
1.429047045 |
\( \frac{33982211}{9216} a^{2} + \frac{23761505}{2304} a + \frac{31103249}{4608} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a\) , \( -18994988706 a^{2} - 35250377819 a + 13302872459\) , \( 3551446969272925 a^{2} + 6590677644352387 a - 2487205798795516\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-18994988706a^{2}-35250377819a+13302872459\right){x}+3551446969272925a^{2}+6590677644352387a-2487205798795516$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$45.55052431$ |
1.429047045 |
\( \frac{834213513193}{2592} a^{2} + \frac{411300264283}{648} a - \frac{186193594877}{1296} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a\) , \( -302810596606 a^{2} - 561947579914 a + 212069130794\) , \( 229055492663050780 a^{2} + 425074885778051045 a - 160415783911913229\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-302810596606a^{2}-561947579914a+212069130794\right){x}+229055492663050780a^{2}+425074885778051045a-160415783911913229$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3 \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$91.10104862$ |
1.429047045 |
\( -\frac{2672626231}{3145728} a^{2} + \frac{190520675}{786432} a + \frac{9809735027}{1572864} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 3\) , \( a\) , \( -263203387702027006291 a^{2} - 488445610550874612765 a + 184330780613944927284\) , \( 545729407092734715052121279424032 a^{2} + 1012749629745456199534075392432429 a - 382193893823557401267991527180675\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-263203387702027006291a^{2}-488445610550874612765a+184330780613944927284\right){x}+545729407092734715052121279424032a^{2}+1012749629745456199534075392432429a-382193893823557401267991527180675$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3 \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$182.2020972$ |
1.429047045 |
\( \frac{3853013}{96} a^{2} - \frac{3041593}{24} a + \frac{1764071}{48} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + a + 10\) , \( -2 a^{2} + 9\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+a+10\right){x}-2a^{2}+9$ |
| 6.1-b1 |
6.1-b |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.148659416$ |
$254.7893170$ |
0.891226412 |
\( \frac{33982211}{9216} a^{2} + \frac{23761505}{2304} a + \frac{31103249}{4608} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - a - 4\) , \( -437084833433259 a^{2} - 811130016953012 a + 306106198877959\) , \( 12396411562145190818833 a^{2} + 23004919757973532876397 a - 8681652010683286994018\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-437084833433259a^{2}-811130016953012a+306106198877959\right){x}+12396411562145190818833a^{2}+23004919757973532876397a-8681652010683286994018$ |
| 6.1-b2 |
6.1-b |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.074329708$ |
$254.7893170$ |
0.891226412 |
\( \frac{834213513193}{2592} a^{2} + \frac{411300264283}{648} a - \frac{186193594877}{1296} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - a - 4\) , \( -6967833527623059 a^{2} - 12930713891379327 a + 4879823943561214\) , \( 799522897971892790041842 a^{2} + 1483732612482169309731139 a - 559934585905588070757801\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-6967833527623059a^{2}-12930713891379327a+4879823943561214\right){x}+799522897971892790041842a^{2}+1483732612482169309731139a-559934585905588070757801$ |
| 6.1-b3 |
6.1-b |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3 \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.297318833$ |
$127.3946585$ |
0.891226412 |
\( \frac{3853013}{96} a^{2} - \frac{3041593}{24} a + \frac{1764071}{48} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - 3\) , \( -367 a^{2} - 680 a + 259\) , \( -4440 a^{2} - 8240 a + 3108\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(-367a^{2}-680a+259\right){x}-4440a^{2}-8240a+3108$ |
| 6.1-b4 |
6.1-b |
$4$ |
$4$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3 \) |
$3.83952$ |
$(-a+3), (a^2-a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.297318833$ |
$63.69732927$ |
0.891226412 |
\( -\frac{2672626231}{3145728} a^{2} + \frac{190520675}{786432} a + \frac{9809735027}{1572864} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -6056450500590472699700624 a^{2} - 11239394326797569935861742 a + 4241549693833829432516231\) , \( 1904879037869682826729875958079326124520 a^{2} + 3535022146945771697732350459284777382011 a - 1334055169621036218710397707677347972626\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-6056450500590472699700624a^{2}-11239394326797569935861742a+4241549693833829432516231\right){x}+1904879037869682826729875958079326124520a^{2}+3535022146945771697732350459284777382011a-1334055169621036218710397707677347972626$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$106.2780682$ |
1.667119771 |
\( \frac{9184611}{1024} a^{2} + \frac{4211329}{256} a - \frac{3281103}{512} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( -63 a^{2} - 112 a + 64\) , \( 504 a^{2} + 952 a - 332\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-63a^{2}-112a+64\right){x}+504a^{2}+952a-332$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{38} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$35.42602274$ |
1.667119771 |
\( \frac{55937378021861251}{1073741824} a^{2} - \frac{9484995877137951}{268435456} a - \frac{173908338277363567}{536870912} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( -428 a^{2} - 772 a + 314\) , \( -12498 a^{2} - 23296 a + 8812\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-428a^{2}-772a+314\right){x}-12498a^{2}-23296a+8812$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{19} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$70.85204548$ |
1.667119771 |
\( -\frac{563151942968223117621}{32768} a^{2} + \frac{95505335836483956729}{8192} a + \frac{1750891961603856400169}{16384} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( 0\) , \( -10 a^{2} - 27 a - 47\) , \( 53 a^{2} + 95 a + 80\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-10a^{2}-27a-47\right){x}+53a^{2}+95a+80$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$212.5561364$ |
1.667119771 |
\( \frac{32018399163}{32} a^{2} + \frac{14856224841}{8} a - \frac{11205136519}{16} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( 0\) , \( -15 a^{2} - 27 a + 13\) , \( 78 a^{2} + 145 a - 54\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-15a^{2}-27a+13\right){x}+78a^{2}+145a-54$ |
| 8.1-b1 |
8.1-b |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{38} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$2.626253715$ |
0.370768081 |
\( \frac{55937378021861251}{1073741824} a^{2} - \frac{9484995877137951}{268435456} a - \frac{173908338277363567}{536870912} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( 32 a^{2} - 20 a - 214\) , \( 316 a^{2} - 200 a - 2012\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(32a^{2}-20a-214\right){x}+316a^{2}-200a-2012$ |
| 8.1-b2 |
8.1-b |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$70.90885031$ |
0.370768081 |
\( \frac{9184611}{1024} a^{2} + \frac{4211329}{256} a - \frac{3281103}{512} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -3 a^{2} + 16\) , \( -2 a^{2} + 12\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-3a^{2}+16\right){x}-2a^{2}+12$ |
| 8.1-b3 |
8.1-b |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{19} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$5.252507431$ |
0.370768081 |
\( -\frac{563151942968223117621}{32768} a^{2} + \frac{95505335836483956729}{8192} a + \frac{1750891961603856400169}{16384} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 55409 a^{2} - 37584 a - 344556\) , \( 12634500 a^{2} - 8570768 a - 78563702\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(55409a^{2}-37584a-344556\right){x}+12634500a^{2}-8570768a-78563702$ |
| 8.1-b4 |
8.1-b |
$4$ |
$6$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$141.8177006$ |
0.370768081 |
\( \frac{32018399163}{32} a^{2} + \frac{14856224841}{8} a - \frac{11205136519}{16} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 684 a^{2} - 464 a - 4256\) , \( 17318 a^{2} - 11748 a - 107688\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(684a^{2}-464a-4256\right){x}+17318a^{2}-11748a-107688$ |
| 8.3-a1 |
8.3-a |
$2$ |
$3$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{38} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$2.452581439$ |
1.384997815 |
\( -\frac{2133363366805}{16384} a^{2} + \frac{13557156967317}{32768} a - \frac{3919110612215}{32768} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 4\) , \( -156 a^{2} + 505 a - 142\) , \( -2427 a^{2} + 7738 a - 2236\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-156a^{2}+505a-142\right){x}-2427a^{2}+7738a-2236$ |
| 8.3-a2 |
8.3-a |
$2$ |
$3$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{18} \) |
$4.02810$ |
$(-a), (-a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$66.21969885$ |
1.384997815 |
\( -\frac{85425}{8} a^{2} - \frac{620411}{32} a + \frac{250371}{32} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 4\) , \( -a^{2} + 5 a + 3\) , \( -3 a^{2} + 11 a - 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-a^{2}+5a+3\right){x}-3a^{2}+11a-1$ |
| 8.3-b1 |
8.3-b |
$2$ |
$3$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{38} \) |
$4.02810$ |
$(-a), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.025771459$ |
$37.38140804$ |
2.720134130 |
\( -\frac{2133363366805}{16384} a^{2} + \frac{13557156967317}{32768} a - \frac{3919110612215}{32768} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 5\) , \( a + 1\) , \( 102 a^{2} + 116 a - 1169\) , \( -3315 a^{2} + 110 a + 26719\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(102a^{2}+116a-1169\right){x}-3315a^{2}+110a+26719$ |
| 8.3-b2 |
8.3-b |
$2$ |
$3$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{18} \) |
$4.02810$ |
$(-a), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.008590486$ |
$112.1442241$ |
2.720134130 |
\( -\frac{85425}{8} a^{2} - \frac{620411}{32} a + \frac{250371}{32} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 5\) , \( a + 1\) , \( -23 a^{2} + 16 a + 136\) , \( 84 a^{2} - 61 a - 513\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-23a^{2}+16a+136\right){x}+84a^{2}-61a-513$ |
| 8.4-a1 |
8.4-a |
$1$ |
$1$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{8} \) |
$4.02810$ |
$(-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.068289439$ |
$90.65692662$ |
2.330713701 |
\( -568 a^{2} - 2129 a - 459 \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - 3\) , \( 235 a^{2} - 159 a - 1458\) , \( 5500 a^{2} - 3730 a - 34199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(235a^{2}-159a-1458\right){x}+5500a^{2}-3730a-34199$ |
| 8.4-b1 |
8.4-b |
$1$ |
$1$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{8} \) |
$4.02810$ |
$(-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.019445950$ |
$240.4507232$ |
1.760312043 |
\( -568 a^{2} - 2129 a - 459 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - 3\) , \( -a + 2\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}-2$ |
| 9.2-a1 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$124.8207572$ |
1.957987718 |
\( -\frac{22454}{3} a^{2} + \frac{17944}{3} a + \frac{136175}{3} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( 39 a^{2} - 26 a - 242\) , \( 182 a^{2} - 124 a - 1133\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(39a^{2}-26a-242\right){x}+182a^{2}-124a-1133$ |
| 9.2-a2 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$124.8207572$ |
1.957987718 |
\( \frac{1193744646928}{9} a^{2} + \frac{2215318490356}{9} a - \frac{836022234811}{9} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -5526499760634851499231902025811048 a^{2} - 10255926313716529782511759228452888 a + 3870406167012859568901758324728498\) , \( 564754336330144768701406435410963748589662355595270 a^{2} + 1048055570364936963298219384612814967889160309049068 a - 395517734705981771586002588485176069098186760346403\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-5526499760634851499231902025811048a^{2}-10255926313716529782511759228452888a+3870406167012859568901758324728498\right){x}+564754336330144768701406435410963748589662355595270a^{2}+1048055570364936963298219384612814967889160309049068a-395517734705981771586002588485176069098186760346403$ |
| 9.2-a3 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$249.6415144$ |
1.957987718 |
\( \frac{10393928}{9} a^{2} - \frac{33027088}{9} a + \frac{9569497}{9} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1220971528 a^{2} - 2265845395 a + 855090191\) , \( 23961109032858 a^{2} + 44466367371685 a - 16780824787114\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1220971528a^{2}-2265845395a+855090191\right){x}+23961109032858a^{2}+44466367371685a-16780824787114$ |
| 9.2-a4 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$62.41037861$ |
1.957987718 |
\( \frac{50342685966374}{3} a^{2} - \frac{159959337664528}{3} a + \frac{46240894748713}{3} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -10263881098 a^{2} - 19047428355 a + 7188164376\) , \( -1412849975253156 a^{2} - 2621928140076144 a + 989469554714251\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10263881098a^{2}-19047428355a+7188164376\right){x}-1412849975253156a^{2}-2621928140076144a+989469554714251$ |
| 9.2-a5 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$62.41037861$ |
1.957987718 |
\( -\frac{6254126064258904}{6561} a^{2} + \frac{4242566608976588}{6561} a + \frac{38889323582756899}{6561} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 4\) , \( -1866825290041603776770 a^{2} - 3464403047951963629328 a + 1307404764002484212199\) , \( 225161615952241938771051489404751 a^{2} + 417848736433901837012872603908652 a - 157688762272927215592404613416570\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-1866825290041603776770a^{2}-3464403047951963629328a+1307404764002484212199\right){x}+225161615952241938771051489404751a^{2}+417848736433901837012872603908652a-157688762272927215592404613416570$ |
| 9.2-a6 |
9.2-a |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$249.6415144$ |
1.957987718 |
\( -\frac{23140480}{81} a^{2} + \frac{36567560}{81} a + \frac{189707497}{81} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 4\) , \( -2359869699331521323690 a^{2} - 4379381307262774256908 a + 1652701462632522183334\) , \( 157480890800299750706659947431708 a^{2} + 292248707467740677131629922293864 a - 110289520915520928068725605981873\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-2359869699331521323690a^{2}-4379381307262774256908a+1652701462632522183334\right){x}+157480890800299750706659947431708a^{2}+292248707467740677131629922293864a-110289520915520928068725605981873$ |
| 9.2-b1 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.30671539$ |
0.637078322 |
\( -\frac{6254126064258904}{6561} a^{2} + \frac{4242566608976588}{6561} a + \frac{38889323582756899}{6561} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -5139152184277137256724317 a^{2} - 9537097330999799398080622 a + 3599132754682129024809192\) , \( 32521911309892493100809364534563929583 a^{2} + 60353268872152501822324084139160939552 a - 22776261928652219308407352445835899805\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-5139152184277137256724317a^{2}-9537097330999799398080622a+3599132754682129024809192\right){x}+32521911309892493100809364534563929583a^{2}+60353268872152501822324084139160939552a-22776261928652219308407352445835899805$ |
| 9.2-b2 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$81.22686159$ |
0.637078322 |
\( -\frac{23140480}{81} a^{2} + \frac{36567560}{81} a + \frac{189707497}{81} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -6496445909868053201674557 a^{2} - 12055925710380953251352602 a + 4549694273456441900087807\) , \( 22746237372184938132373043105438273797 a^{2} + 42211841944716846720244988567107001704 a - 15930006552923432511991276383170096698\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-6496445909868053201674557a^{2}-12055925710380953251352602a+4549694273456441900087807\right){x}+22746237372184938132373043105438273797a^{2}+42211841944716846720244988567107001704a-15930006552923432511991276383170096698$ |
| 9.2-b3 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$40.61343079$ |
0.637078322 |
\( \frac{1193744646928}{9} a^{2} + \frac{2215318490356}{9} a - \frac{836022234811}{9} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -15213808955652578169291843354038879246 a^{2} - 28233368381112438066908189198934418748 a + 10654776541408736118194617775456855751\) , \( 81572031540889384448956329015783007414611138369481687719 a^{2} + 151379133444026222773615726522089054559145289953096921261 a - 57127821877505715123625263237560145609395863180432794534\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-15213808955652578169291843354038879246a^{2}-28233368381112438066908189198934418748a+10654776541408736118194617775456855751\right){x}+81572031540889384448956329015783007414611138369481687719a^{2}+151379133444026222773615726522089054559145289953096921261a-57127821877505715123625263237560145609395863180432794534$ |
| 9.2-b4 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$81.22686159$ |
0.637078322 |
\( \frac{10393928}{9} a^{2} - \frac{33027088}{9} a + \frac{9569497}{9} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( -3361192142751 a^{2} - 6237607968037 a + 2353963514215\) , \( 3460803344243224356 a^{2} + 6422463697120460875 a - 2423724814355008420\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-3361192142751a^{2}-6237607968037a+2353963514215\right){x}+3460803344243224356a^{2}+6422463697120460875a-2423724814355008420$ |
| 9.2-b5 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.15335769$ |
0.637078322 |
\( \frac{50342685966374}{3} a^{2} - \frac{159959337664528}{3} a + \frac{46240894748713}{3} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( -28255266974921 a^{2} - 52435347619717 a + 19788177741240\) , \( -204070120207568794276 a^{2} - 378707718507107467050 a + 142917630681974075237\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-28255266974921a^{2}-52435347619717a+19788177741240\right){x}-204070120207568794276a^{2}-378707718507107467050a+142917630681974075237$ |
| 9.2-b6 |
9.2-b |
$6$ |
$8$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.10796$ |
$(a^2-a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$81.22686159$ |
0.637078322 |
\( -\frac{22454}{3} a^{2} + \frac{17944}{3} a + \frac{136175}{3} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( 4 a^{2} + 10 a + 7\) , \( 11 a^{2} + 24 a - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(4a^{2}+10a+7\right){x}+11a^{2}+24a-2$ |
| 12.1-a1 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$31.38748448$ |
1.477069450 |
\( \frac{767765770888643}{36864} a^{2} + \frac{356193608746913}{9216} a - \frac{268832552819119}{18432} \) |
\( \bigl[a^{2} - a - 3\) , \( 1\) , \( a + 1\) , \( 57167 a^{2} - 38782 a - 355472\) , \( -13151176 a^{2} + 8921268 a + 81776467\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(57167a^{2}-38782a-355472\right){x}-13151176a^{2}+8921268a+81776467$ |
| 12.1-a2 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{4} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.923435560$ |
1.477069450 |
\( \frac{28680482699892979305475847}{5184} a^{2} + \frac{13306112817877625586780929}{1296} a - \frac{10042985788695646918388803}{2592} \) |
\( \bigl[a^{2} - a - 3\) , \( 1\) , \( a + 1\) , \( 39197 a^{2} - 26592 a - 243732\) , \( -21633056 a^{2} + 14675060 a + 134518379\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(39197a^{2}-26592a-243732\right){x}-21633056a^{2}+14675060a+134518379$ |
| 12.1-a3 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$31.38748448$ |
1.477069450 |
\( -\frac{4929322714393}{96} a^{2} + \frac{1671929742829}{48} a + \frac{61302855066215}{192} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 5\) , \( 1\) , \( 7982841864 a^{2} - 5415263165 a - 49638801124\) , \( -690834441982159 a^{2} + 468636404179256 a + 4295737540690083\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(7982841864a^{2}-5415263165a-49638801124\right){x}-690834441982159a^{2}+468636404179256a+4295737540690083$ |
| 12.1-a4 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3 \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$31.38748448$ |
1.477069450 |
\( \frac{19526696771202314825}{50331648} a^{2} - \frac{15511076285266340125}{12582912} a + \frac{8967854540137295603}{25165824} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 5\) , \( 1\) , \( -109 a^{2} + 330 a - 78\) , \( 1316 a^{2} - 4197 a + 1221\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-109a^{2}+330a-78\right){x}+1316a^{2}-4197a+1221$ |
| 12.1-a5 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$94.16245344$ |
1.477069450 |
\( -\frac{5004517}{11664} a^{2} + \frac{2632469}{2916} a + \frac{47382317}{5832} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -5635 a^{2} - 10459 a + 3945\) , \( -510983 a^{2} - 948268 a + 357859\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5635a^{2}-10459a+3945\right){x}-510983a^{2}-948268a+357859$ |
| 12.1-a6 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{3} \cdot 3^{12} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$11.77030668$ |
1.477069450 |
\( \frac{8749450000313}{2125764} a^{2} + \frac{3432109524343}{1062882} a - \frac{1556232857809}{1062882} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -86920 a^{2} - 161304 a + 60875\) , \( -35286317 a^{2} - 65483378 a + 24712271\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-86920a^{2}-161304a+60875\right){x}-35286317a^{2}-65483378a+24712271$ |
| 12.1-a7 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{3} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$94.16245344$ |
1.477069450 |
\( -\frac{61321}{54} a^{2} + \frac{18883}{27} a + \frac{814559}{108} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( 8158 a^{2} - 5530 a - 50714\) , \( -618317 a^{2} + 419416 a + 3844749\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(8158a^{2}-5530a-50714\right){x}-618317a^{2}+419416a+3844749$ |
| 12.1-a8 |
12.1-a |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{3} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$94.16245344$ |
1.477069450 |
\( -\frac{63031725775}{6912} a^{2} + \frac{10686570875}{1728} a + \frac{196019581547}{3456} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -6522922 a^{2} - 12105060 a + 4568240\) , \( 20564626474 a^{2} + 38163268421 a - 14402146127\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-6522922a^{2}-12105060a+4568240\right){x}+20564626474a^{2}+38163268421a-14402146127$ |
| 12.1-b1 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$6.400037789$ |
0.903541694 |
\( \frac{767765770888643}{36864} a^{2} + \frac{356193608746913}{9216} a - \frac{268832552819119}{18432} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 333088755 a^{2} - 225955030 a - 2071208065\) , \( 5879094630820 a^{2} - 3988159246537 a - 36557308055487\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(333088755a^{2}-225955030a-2071208065\right){x}+5879094630820a^{2}-3988159246537a-36557308055487$ |
| 12.1-b2 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{4} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$1.600009447$ |
0.903541694 |
\( \frac{28680482699892979305475847}{5184} a^{2} + \frac{13306112817877625586780929}{1296} a - \frac{10042985788695646918388803}{2592} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 228386865 a^{2} - 154929160 a - 1420152165\) , \( 9641929510302 a^{2} - 6540726548163 a - 59955317866391\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(228386865a^{2}-154929160a-1420152165\right){x}+9641929510302a^{2}-6540726548163a-59955317866391$ |
| 12.1-b3 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3 \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.200018894$ |
0.903541694 |
\( -\frac{4929322714393}{96} a^{2} + \frac{1671929742829}{48} a + \frac{61302855066215}{192} \) |
\( \bigl[a^{2} - a - 3\) , \( 0\) , \( 1\) , \( 46512244972505 a^{2} - 31552177930907 a - 289221823186578\) , \( 307256602036167686328 a^{2} - 208431456783512664924 a - 1910578917004437407558\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(46512244972505a^{2}-31552177930907a-289221823186578\right){x}+307256602036167686328a^{2}-208431456783512664924a-1910578917004437407558$ |
| 12.1-b4 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3 \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$6.400037789$ |
0.903541694 |
\( \frac{19526696771202314825}{50331648} a^{2} - \frac{15511076285266340125}{12582912} a + \frac{8967854540137295603}{25165824} \) |
\( \bigl[a^{2} - a - 3\) , \( 0\) , \( 1\) , \( 3100 a^{2} - 1980 a - 19628\) , \( 36343 a^{2} - 23309 a - 229828\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(3100a^{2}-1980a-19628\right){x}+36343a^{2}-23309a-229828$ |
| 12.1-b5 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$172.8010203$ |
0.903541694 |
\( -\frac{5004517}{11664} a^{2} + \frac{2632469}{2916} a + \frac{47382317}{5832} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( 1385 a^{2} - 944 a - 8621\) , \( -46274 a^{2} + 31374 a + 287704\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(1385a^{2}-944a-8621\right){x}-46274a^{2}+31374a+287704$ |
| 12.1-b6 |
12.1-b |
$8$ |
$12$ |
3.3.1016.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{3} \cdot 3^{12} \) |
$4.30972$ |
$(-a), (-a+3), (a^2-a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$43.20025507$ |
0.903541694 |
\( \frac{8749450000313}{2125764} a^{2} + \frac{3432109524343}{1062882} a - \frac{1556232857809}{1062882} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( -2020 a^{2} + 1291 a + 12389\) , \( -225678 a^{2} + 152356 a + 1401706\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-2020a^{2}+1291a+12389\right){x}-225678a^{2}+152356a+1401706$ |
*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.
