| 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 |
| 1.1-a1 |
1.1-a |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$2.96505$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.010217839$ |
$490.9702338$ |
0.453567406 |
\( -1805 a^{2} - 867 a + 14820 \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( a^{2} + a - 7\) , \( -4 a^{2} - 8 a + 26\) , \( 10 a^{2} + 14 a - 45\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-4a^{2}-8a+26\right){x}+10a^{2}+14a-45$ |
| 2.1-a1 |
2.1-a |
$2$ |
$2$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{9} \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1.573294186$ |
$36.31363158$ |
1.291359688 |
\( \frac{2921602999}{512} a^{2} - \frac{12034022259}{512} a + \frac{11240130237}{512} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( 0\) , \( a^{2} + 6 a - 10\) , \( 8 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(a^{2}+6a-10\right){x}+8a-12$ |
| 2.1-a2 |
2.1-a |
$2$ |
$2$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{18} \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.786647093$ |
$36.31363158$ |
1.291359688 |
\( -\frac{24440916577}{262144} a^{2} - \frac{9515099643}{262144} a + \frac{205063385781}{262144} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( 0\) , \( -258049030 a^{2} - 435431820 a + 1152261988\) , \( 3966553778797 a^{2} + 6693161107945 a - 17711785781052\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(-258049030a^{2}-435431820a+1152261988\right){x}+3966553778797a^{2}+6693161107945a-17711785781052$ |
| 2.1-b1 |
2.1-b |
$4$ |
$6$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.123055757$ |
$355.8523148$ |
0.989781515 |
\( \frac{5113927}{8} a^{2} - \frac{20892459}{8} a + \frac{19220253}{8} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - a + 8\) , \( a^{2} + 2 a - 7\) , \( 2796 a^{2} + 4704 a - 12528\) , \( 151105 a^{2} + 254999 a - 674650\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(2796a^{2}+4704a-12528\right){x}+151105a^{2}+254999a-674650$ |
| 2.1-b2 |
2.1-b |
$4$ |
$6$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.061527878$ |
$355.8523148$ |
0.989781515 |
\( -\frac{8056656673}{64} a^{2} - \frac{3477399675}{64} a + \frac{67531474101}{64} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - a + 8\) , \( a^{2} + 2 a - 7\) , \( -25680784166745 a^{2} - 43333743948014 a + 114671973006422\) , \( 90272361932296302604 a^{2} + 152325543961446012632 a - 403091657307452480584\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(-25680784166745a^{2}-43333743948014a+114671973006422\right){x}+90272361932296302604a^{2}+152325543961446012632a-403091657307452480584$ |
| 2.1-b3 |
2.1-b |
$4$ |
$6$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.369167273$ |
$118.6174382$ |
0.989781515 |
\( -\frac{791}{2} a^{2} - \frac{1587}{2} a + \frac{7053}{2} \) |
\( \bigl[1\) , \( -a^{2} - a + 8\) , \( a^{2} + a - 7\) , \( -10 a^{2} + 33 a - 17\) , \( -26 a^{2} + 104 a - 94\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(-10a^{2}+33a-17\right){x}-26a^{2}+104a-94$ |
| 2.1-b4 |
2.1-b |
$4$ |
$6$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$3.32816$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.184583636$ |
$118.6174382$ |
0.989781515 |
\( \frac{2460287}{4} a^{2} + \frac{4151937}{4} a - \frac{10978971}{4} \) |
\( \bigl[1\) , \( -a^{2} - a + 8\) , \( a^{2} + a - 7\) , \( -882517 a^{2} - 1489157 a + 3940695\) , \( -861016809 a^{2} - 1452879386 a + 3844683856\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(-882517a^{2}-1489157a+3940695\right){x}-861016809a^{2}-1452879386a+3844683856$ |
| 3.2-a1 |
3.2-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{15} \) |
$3.56084$ |
$(a^2-7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$43.43185663$ |
2.181541530 |
\( -\frac{243799306240}{14348907} a^{2} + \frac{327765458944}{4782969} a - \frac{294414221312}{4782969} \) |
\( \bigl[0\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 7\) , \( -6 a^{2} - 3 a + 49\) , \( 2 a^{2} - 4 a - 35\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(-6a^{2}-3a+49\right){x}+2a^{2}-4a-35$ |
| 3.2-a2 |
3.2-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{5} \) |
$3.56084$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$1$ |
$14.47728554$ |
2.181541530 |
\( -\frac{5817118720}{243} a^{2} - \frac{3272155136}{81} a + \frac{8657698816}{81} \) |
\( \bigl[0\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 7\) , \( -120593375573 a^{2} - 203489209238 a + 538483568369\) , \( -43525777755792341 a^{2} - 73445378309351503 a + 194354922322031762\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(-120593375573a^{2}-203489209238a+538483568369\right){x}-43525777755792341a^{2}-73445378309351503a+194354922322031762$ |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$3.73573$ |
$(a^2+a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$1.681802103$ |
$2.012801461$ |
0.612115562 |
\( -\frac{735246802754149}{1024} a^{2} - \frac{79339028615369}{256} a + \frac{96294991127641}{16} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -1\) , \( 1\) , \( -40721924 a^{2} - 68714164 a + 181834900\) , \( -270230459609 a^{2} - 455986759126 a + 1206655519842\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-40721924a^{2}-68714164a+181834900\right){x}-270230459609a^{2}-455986759126a+1206655519842$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$3.73573$ |
$(a^2+a-7)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$0.336360420$ |
$251.6001826$ |
0.612115562 |
\( -\frac{343}{2} a^{2} + \frac{1943}{4} a + 1543 \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{2} + 2 a - 7\) , \( 3 a^{2} - 28\) , \( -6 a^{2} - 4 a + 46\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{2}-28\right){x}-6a^{2}-4a+46$ |
| 4.2-a1 |
4.2-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.73573$ |
$(a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$91.17798647$ |
0.915956993 |
\( -7443441582 a^{2} - 3212791161 a + 62391456220 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 6\) , \( 188 a^{2} + 89 a - 1554\) , \( -2456 a^{2} - 1044 a + 20635\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(188a^{2}+89a-1554\right){x}-2456a^{2}-1044a+20635$ |
| 4.2-a2 |
4.2-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.73573$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$30.39266215$ |
0.915956993 |
\( -15429 a^{2} + 1908 a + 33184 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4885896171 a^{2} - 8244459484 a + 21816908547\) , \( -359131445660112 a^{2} - 605998244007084 a + 1603623595585837\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4885896171a^{2}-8244459484a+21816908547\right){x}-359131445660112a^{2}-605998244007084a+1603623595585837$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{8} \) |
$3.99691$ |
$(a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.162784343$ |
$173.8695930$ |
1.279481083 |
\( \frac{29923}{162} a^{2} - \frac{19195}{54} a - \frac{63187}{162} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a + 1\) , \( a\) , \( -12815463 a^{2} + 52787238 a - 49305624\) , \( -50792903895 a^{2} + 209217326538 a - 195418286610\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-12815463a^{2}+52787238a-49305624\right){x}-50792903895a^{2}+209217326538a-195418286610$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{2} \) |
$3.99691$ |
$(a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.162784343$ |
$86.93479650$ |
1.279481083 |
\( -\frac{12427210626707}{48} a^{2} - \frac{1787973677179}{16} a + \frac{104165760846863}{48} \) |
\( \bigl[1\) , \( a^{2} - 8\) , \( a^{2} + a - 7\) , \( -5 a^{2} + 52 a - 105\) , \( -186 a^{2} + 572 a - 196\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(-5a^{2}+52a-105\right){x}-186a^{2}+572a-196$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{2} \) |
$3.99691$ |
$(a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.651137374$ |
$43.46739825$ |
1.279481083 |
\( \frac{1669232982931}{6} a^{2} - \frac{2268686450851}{2} a + \frac{6322552321817}{6} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -801934 a^{2} + 3303175 a - 3085301\) , \( -1420574725 a^{2} + 5851385188 a - 5465453961\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-801934a^{2}+3303175a-3085301\right){x}-1420574725a^{2}+5851385188a-5465453961$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{4} \) |
$3.99691$ |
$(a-2), (-a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.325568687$ |
$173.8695930$ |
1.279481083 |
\( -\frac{3386197}{36} a^{2} - \frac{5821025}{12} a + \frac{75756205}{36} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -50124 a^{2} + 206470 a - 192851\) , \( -22179850 a^{2} + 91359400 a - 85333743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-50124a^{2}+206470a-192851\right){x}-22179850a^{2}+91359400a-85333743$ |
| 6.2-a1 |
6.2-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{12} \) |
$3.99691$ |
$(a-2), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$13.64801496$ |
2.467897288 |
\( -\frac{10068267494756371}{4251528} a^{2} - \frac{1448583377612939}{1417176} a + \frac{28130990721363037}{1417176} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + a - 7\) , \( a + 1\) , \( 12 a^{2} + 72 a - 252\) , \( -20 a^{2} + 483 a - 1111\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(12a^{2}+72a-252\right){x}-20a^{2}+483a-1111$ |
| 6.2-a2 |
6.2-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$3.99691$ |
$(a-2), (a^2-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$109.1841196$ |
2.467897288 |
\( -\frac{933844577}{46656} a^{2} - \frac{138653353}{15552} a + \frac{2657273255}{15552} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + a - 7\) , \( a + 1\) , \( 2 a^{2} + 17 a - 32\) , \( 10 a^{2} - 4 a - 19\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(2a^{2}+17a-32\right){x}+10a^{2}-4a-19$ |
| 6.2-a3 |
6.2-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{3} \) |
$3.99691$ |
$(a-2), (a^2-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$109.1841196$ |
2.467897288 |
\( \frac{42181128005}{110592} a^{2} - \frac{56401359443}{36864} a + \frac{51927819229}{36864} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + a - 7\) , \( a + 1\) , \( -11039040 a^{2} - 18627270 a + 49292442\) , \( 37436377478 a^{2} + 63170126949 a - 167164025825\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(-11039040a^{2}-18627270a+49292442\right){x}+37436377478a^{2}+63170126949a-167164025825$ |
| 6.2-a4 |
6.2-a |
$4$ |
$4$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$3.99691$ |
$(a-2), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$109.1841196$ |
2.467897288 |
\( \frac{63163265}{216} a^{2} + \frac{35546185}{72} a - \frac{93906431}{72} \) |
\( \bigl[1\) , \( -a^{2} + 8\) , \( a^{2} + a - 6\) , \( 1321 a^{2} - 5457 a + 5119\) , \( 118877 a^{2} - 489670 a + 457387\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}+8\right){x}^{2}+\left(1321a^{2}-5457a+5119\right){x}+118877a^{2}-489670a+457387$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$45.32400681$ |
1.365949478 |
\( -1805 a^{2} - 867 a + 14820 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} + 6\) , \( a^{2} + a - 7\) , \( 2 a^{2} + 4 a - 6\) , \( 3 a^{2} + 5 a - 14\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(2a^{2}+4a-6\right){x}+3a^{2}+5a-14$ |
| 9.2-a1 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$43.03654638$ |
2.594022559 |
\( -60143857827860 a^{2} - 25959721992226 a + \frac{1512390263245325}{3} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( 5464793538937572689 a^{2} + 9221290222581932701 a - 24401850547629406544\) , \( -68789450003598568026751023013 a^{2} - 116075287788144641711366865332 a + 307164372502126991187472442669\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(5464793538937572689a^{2}+9221290222581932701a-24401850547629406544\right){x}-68789450003598568026751023013a^{2}-116075287788144641711366865332a+307164372502126991187472442669$ |
| 9.2-a2 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{3} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$172.1461855$ |
2.594022559 |
\( -\frac{20242}{9} a^{2} - 886 a + \frac{57505}{3} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( 2 a^{2} + a - 5\) , \( 4 a^{2} + 2 a - 13\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(2a^{2}+a-5\right){x}+4a^{2}+2a-13$ |
| 9.2-a3 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$344.2923710$ |
2.594022559 |
\( \frac{28768}{81} a^{2} - \frac{49600}{27} a + \frac{188963}{27} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( -769355527 a^{2} - 1298210181 a + 3435390280\) , \( 17553334852911 a^{2} + 29619489537808 a - 78380610473437\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-769355527a^{2}-1298210181a+3435390280\right){x}+17553334852911a^{2}+29619489537808a-78380610473437$ |
| 9.2-a4 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$172.1461855$ |
2.594022559 |
\( \frac{72291167014}{6561} a^{2} - \frac{73710551386}{2187} a + \frac{56138792327}{2187} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( -11582375332 a^{2} - 19544095061 a + 51718585495\) , \( 1295439685454946 a^{2} + 2185924357492320 a - 5784505008781219\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-11582375332a^{2}-19544095061a+51718585495\right){x}+1295439685454946a^{2}+2185924357492320a-5784505008781219$ |
| 9.2-a5 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$172.1461855$ |
2.594022559 |
\( -\frac{9726188}{3} a^{2} - \frac{4192564}{3} a + \frac{244668025}{9} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( -6474374190643825486 a^{2} - 10924856171808384089 a + 28909914027645847891\) , \( -16111446760871726059239518746 a^{2} - 27186448203230642548320219338 a + 71942171861320324465755079349\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-6474374190643825486a^{2}-10924856171808384089a+28909914027645847891\right){x}-16111446760871726059239518746a^{2}-27186448203230642548320219338a+71942171861320324465755079349$ |
| 9.2-a6 |
9.2-a |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$43.03654638$ |
2.594022559 |
\( \frac{2279981180}{81} a^{2} + \frac{1282388222}{27} a - \frac{10180946903}{81} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 6\) , \( a^{2} + 2 a - 7\) , \( -166535676473386919713863599407 a^{2} - 281012227494630266954046819613 a + 743628951248907015423800245990\) , \( -70634543923534110128635120519384006572877273 a^{2} - 119188698460005953835977449817583843251104538 a + 315403239306482054442397569329892631172395913\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-166535676473386919713863599407a^{2}-281012227494630266954046819613a+743628951248907015423800245990\right){x}-70634543923534110128635120519384006572877273a^{2}-119188698460005953835977449817583843251104538a+315403239306482054442397569329892631172395913$ |
| 9.2-b1 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.518021199$ |
$157.0194855$ |
1.346911309 |
\( -1470519 a^{2} - \frac{16022218}{27} a + \frac{337083187}{27} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( 1\) , \( a + 1\) , \( -168042450 a^{2} - 283554756 a + 750357125\) , \( -2257279020556 a^{2} - 3808931630003 a + 10079389991852\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-168042450a^{2}-283554756a+750357125\right){x}-2257279020556a^{2}-3808931630003a+10079389991852$ |
| 9.2-b2 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.036042399$ |
$78.50974279$ |
1.346911309 |
\( -\frac{117032992943786}{9} a^{2} - \frac{50514612962635}{9} a + 108997649659333 \) |
\( \bigl[a^{2} + 2 a - 7\) , \( 1\) , \( a + 1\) , \( -149591811451881930 a^{2} - 252421157083225867 a + 667969796148538372\) , \( -285561321981548313522415795 a^{2} - 481856049560466949841977343 a + 1275112161425212047229010976\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-149591811451881930a^{2}-252421157083225867a+667969796148538372\right){x}-285561321981548313522415795a^{2}-481856049560466949841977343a+1275112161425212047229010976$ |
| 9.2-b3 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.759010599$ |
$314.0389711$ |
1.346911309 |
\( \frac{286462502}{9} a^{2} - \frac{1179918125}{9} a + 122451275 \) |
\( \bigl[1\) , \( a^{2} + 2 a - 8\) , \( a^{2} + 2 a - 6\) , \( -11479023909 a^{2} - 19369699887 a + 51257092089\) , \( 24949115909547 a^{2} + 42099127251321 a - 111404867060616\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-8\right){x}^{2}+\left(-11479023909a^{2}-19369699887a+51257092089\right){x}+24949115909547a^{2}+42099127251321a-111404867060616$ |
| 9.2-b4 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.072084798$ |
$2.453429462$ |
1.346911309 |
\( \frac{25156068307}{177147} a^{2} - \frac{424607138560}{531441} a + \frac{453585178543}{531441} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -12125 a^{2} + 49927 a - 46606\) , \( -2648506 a^{2} + 10909219 a - 10189612\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-12125a^{2}+49927a-46606\right){x}-2648506a^{2}+10909219a-10189612$ |
| 9.2-b5 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.036042399$ |
$19.62743569$ |
1.346911309 |
\( \frac{7224552154312}{729} a^{2} + \frac{12190706256901}{729} a - \frac{32259668489219}{729} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -840 a^{2} + 3467 a - 3251\) , \( -32139 a^{2} + 132382 a - 123652\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-840a^{2}+3467a-3251\right){x}-32139a^{2}+132382a-123652$ |
| 9.2-b6 |
9.2-b |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.072084798$ |
$2.453429462$ |
1.346911309 |
\( 716121490152889516023 a^{2} + \frac{32626343393113713869056}{27} a - \frac{86337501171444458105557}{27} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2445 a^{2} - 10033 a + 9304\) , \( -215496 a^{2} + 887761 a - 829432\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2445a^{2}-10033a+9304\right){x}-215496a^{2}+887761a-829432$ |
| 9.2-c1 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$87.43115688$ |
1.317475566 |
\( \frac{824}{3} a^{2} + \frac{451}{3} a - \frac{2125}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -2 a^{2} - 2 a + 19\) , \( -2 a^{2} + a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-2a^{2}-2a+19\right){x}-2a^{2}+a+12$ |
| 9.2-c2 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$174.8623137$ |
1.317475566 |
\( -\frac{19783}{9} a^{2} - \frac{8870}{9} a + \frac{182713}{9} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -702432799 a^{2} - 1185284794 a + 3136561354\) , \( 3239249690901 a^{2} + 5465908508783 a - 14464167087117\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-702432799a^{2}-1185284794a+3136561354\right){x}+3239249690901a^{2}+5465908508783a-14464167087117$ |
| 9.2-c3 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$87.43115688$ |
1.317475566 |
\( -\frac{875364316}{27} a^{2} - \frac{1127612497}{81} a + \frac{22037525167}{81} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -8385560479 a^{2} - 14149791074 a + 37443901979\) , \( 796733238814695 a^{2} + 1344407317996561 a - 3557639512153394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-8385560479a^{2}-14149791074a+37443901979\right){x}+796733238814695a^{2}+1344407317996561a-3557639512153394$ |
| 9.2-c4 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$87.43115688$ |
1.317475566 |
\( \frac{5080288}{81} a^{2} - \frac{3496249}{27} a + \frac{1663991}{27} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -11481073085342064183 a^{2} - 19373157692467176296 a + 51266242275896509917\) , \( -40222381554819422474259467243 a^{2} - 67871229007587441991932804609 a + 179604322903888845344109610512\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-11481073085342064183a^{2}-19373157692467176296a+51266242275896509917\right){x}-40222381554819422474259467243a^{2}-67871229007587441991932804609a+179604322903888845344109610512$ |
| 9.2-c5 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$21.85778922$ |
1.317475566 |
\( \frac{24734697256525}{6561} a^{2} + \frac{13920127845488}{2187} a - \frac{36791828642323}{2187} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -183431728828873285368 a^{2} - 309522618834349402156 a + 819074609256996306162\) , \( -2582080159773731860650014367176 a^{2} - 4357000929969863968119780089375 a + 11529719048278473986642546472741\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-183431728828873285368a^{2}-309522618834349402156a+819074609256996306162\right){x}-2582080159773731860650014367176a^{2}-4357000929969863968119780089375a+11529719048278473986642546472741$ |
| 9.2-c6 |
9.2-c |
$6$ |
$8$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{3} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$21.85778922$ |
1.317475566 |
\( \frac{393566098067}{9} a^{2} - 180123251160 a + \frac{504729380899}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a\) , \( -7938473571437688826182778922 a^{2} - 13395376825298152072185077758 a + 35447532333342050532329273192\) , \( -5703317862305540240087992768208043766817812 a^{2} - 9623776061296458474087351061537487220276973 a + 25466929191374681740077766040276820475568335\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-7938473571437688826182778922a^{2}-13395376825298152072185077758a+35447532333342050532329273192\right){x}-5703317862305540240087992768208043766817812a^{2}-9623776061296458474087351061537487220276973a+25466929191374681740077766040276820475568335$ |
| 9.2-d1 |
9.2-d |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.27634$ |
$(-a+3), (a^2-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.364258997$ |
$44.80641055$ |
2.951263810 |
\( -\frac{65536}{27} a^{2} + \frac{241664}{27} a - \frac{176128}{27} \) |
\( \bigl[0\) , \( -1\) , \( a^{2} + 2 a - 7\) , \( -3 a^{2} + 22\) , \( 2 a^{2} + a - 25\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}-{x}^{2}+\left(-3a^{2}+22\right){x}+2a^{2}+a-25$ |
| 9.3-a1 |
9.3-a |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.27634$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$45.32400681$ |
1.365949478 |
\( -1805 a^{2} - 867 a + 14820 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 0\) , \( a^{2} + a - 7\) , \( a^{2} + 21 a - 34\) , \( -83 a^{2} + 380 a - 377\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}+21a-34\right){x}-83a^{2}+380a-377$ |
| 9.3-b1 |
9.3-b |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.27634$ |
$(a^2-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.180702744$ |
$49.62331419$ |
1.621466966 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 7\) , \( 2 a^{2} + 3 a - 8\) , \( 2 a - 4\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(2a^{2}+3a-8\right){x}+2a-4$ |
| 9.3-b2 |
9.3-b |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.27634$ |
$(a^2-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.060234248$ |
$148.8699425$ |
1.621466966 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} - 2 a + 6\) , \( a^{2} + 2 a - 7\) , \( 2 a^{2} + 3 a - 8\) , \( 205375621883 a^{2} + 346550734357 a - 917060305319\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(2a^{2}+3a-8\right){x}+205375621883a^{2}+346550734357a-917060305319$ |
| 9.3-c1 |
9.3-c |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{21} \) |
$4.27634$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$12.24623230$ |
0.738140151 |
\( -\frac{243799306240}{14348907} a^{2} + \frac{327765458944}{4782969} a - \frac{294414221312}{4782969} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} + 2 a - 7\) , \( -108 a^{2} + 445 a - 415\) , \( -2381 a^{2} + 9802 a - 9154\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-108a^{2}+445a-415\right){x}-2381a^{2}+9802a-9154$ |
| 9.3-c2 |
9.3-c |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{11} \) |
$4.27634$ |
$(a^2-7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$110.2160907$ |
0.738140151 |
\( -\frac{5817118720}{243} a^{2} - \frac{3272155136}{81} a + \frac{8657698816}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} + 2 a - 7\) , \( -1037315816 a^{2} - 1750366258 a + 4631908833\) , \( 34724339492067 a^{2} + 58593835240498 a - 155054008282845\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1037315816a^{2}-1750366258a+4631908833\right){x}+34724339492067a^{2}+58593835240498a-155054008282845$ |
| 12.1-a1 |
12.1-a |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3^{3} \) |
$4.48638$ |
$(-a+3), (a^2+a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.371048074$ |
$15.81105312$ |
1.959932327 |
\( -\frac{2238055}{18} a^{2} + \frac{4630214}{9} a - 484609 \) |
\( \bigl[1\) , \( a^{2} + 2 a - 8\) , \( a^{2} + a - 7\) , \( 2 a^{2} + 3 a - 4\) , \( -100 a^{2} - 169 a + 443\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}+2a-8\right){x}^{2}+\left(2a^{2}+3a-4\right){x}-100a^{2}-169a+443$ |
| 12.1-b1 |
12.1-b |
$1$ |
$1$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$4.48638$ |
$(-a+3), (a^2+a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.217650674$ |
$77.40051676$ |
1.523110713 |
\( -\frac{1747}{6} a^{2} - \frac{2759}{6} a + 2973 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -2 a + 4\) , \( -a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+4\right){x}-a+2$ |
| 16.1-a1 |
16.1-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$4.70673$ |
$(a-2), (a^2+a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$18.15763730$ |
3.283348091 |
\( -\frac{529699373}{16} a^{2} - \frac{228606915}{16} a + \frac{1109979033}{4} \) |
\( \bigl[a^{2} + a - 6\) , \( a^{2} + 2 a - 6\) , \( a^{2} + a - 6\) , \( 130 a^{2} + 218 a - 583\) , \( 2833 a^{2} + 4780 a - 12652\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(130a^{2}+218a-583\right){x}+2833a^{2}+4780a-12652$ |
| 16.1-a2 |
16.1-a |
$2$ |
$3$ |
3.3.1101.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{32} \) |
$4.70673$ |
$(a-2), (a^2+a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$54.47291191$ |
3.283348091 |
\( -\frac{162366149}{4096} a^{2} - \frac{273956835}{4096} a + \frac{183018201}{1024} \) |
\( \bigl[a\) , \( -a^{2} - 2 a + 6\) , \( a\) , \( -53814471028 a^{2} - 90806514833 a + 240296851088\) , \( 13014025921440557 a^{2} + 21959861636261994 a - 58111310755887520\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(-53814471028a^{2}-90806514833a+240296851088\right){x}+13014025921440557a^{2}+21959861636261994a-58111310755887520$ |
*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.
