| 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 |
| 8.1-a1 |
8.1-a |
$2$ |
$7$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{21} \) |
$3.33634$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 7 \) |
$1$ |
$4.892617900$ |
1.297247824 |
\( -\frac{8566225627259849}{16} a^{2} + \frac{74218209683324901}{64} a + \frac{158193447384814707}{128} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -638 a^{2} - 1825 a - 1037\) , \( 25901 a^{2} + 76595 a + 44088\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-638a^{2}-1825a-1037\right){x}+25901a^{2}+76595a+44088$ |
| 8.1-a2 |
8.1-a |
$2$ |
$7$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$3.33634$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$34.24832530$ |
1.297247824 |
\( \frac{351863}{2} a^{2} - 137467 a - 1123151 \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 2 a^{2} + 5 a + 3\) , \( -a^{2} - 3 a - 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(2a^{2}+5a+3\right){x}-a^{2}-3a-2$ |
| 8.1-b1 |
8.1-b |
$2$ |
$7$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$3.33634$ |
$(2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$171.6162651$ |
1.193956451 |
\( \frac{351863}{2} a^{2} - 137467 a - 1123151 \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 4\) , \( 3 a^{2} - 6 a - 11\) , \( 2 a^{2} - 5 a - 8\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(3a^{2}-6a-11\right){x}+2a^{2}-5a-8$ |
| 8.1-b2 |
8.1-b |
$2$ |
$7$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{21} \) |
$3.33634$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$9$ |
\( 7 \) |
$1$ |
$0.500338965$ |
1.193956451 |
\( -\frac{8566225627259849}{16} a^{2} + \frac{74218209683324901}{64} a + \frac{158193447384814707}{128} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 4\) , \( -427 a^{2} + 794 a + 879\) , \( -9484 a^{2} + 19447 a + 21032\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-427a^{2}+794a+879\right){x}-9484a^{2}+19447a+21032$ |
| 11.2-a1 |
11.2-a |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$3.51820$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$2.746811439$ |
1.664686436 |
\( -\frac{21122737673865178}{14641} a^{2} + \frac{34361275652236931}{14641} a + \frac{173526626002163266}{14641} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 507 a^{2} - 423 a - 3295\) , \( 9687 a^{2} - 7710 a - 62162\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(507a^{2}-423a-3295\right){x}+9687a^{2}-7710a-62162$ |
| 11.2-a2 |
11.2-a |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{16} \) |
$3.51820$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.98724575$ |
1.664686436 |
\( -\frac{11805919766521078150}{45949729863572161} a^{2} + \frac{23778098342787800525}{45949729863572161} a + \frac{145448866834889845358}{45949729863572161} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 37 a^{2} - 33 a - 235\) , \( 79 a^{2} - 66 a - 504\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(37a^{2}-33a-235\right){x}+79a^{2}-66a-504$ |
| 11.2-a3 |
11.2-a |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$3.51820$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$21.97449151$ |
1.664686436 |
\( -\frac{97386354175171}{214358881} a^{2} + \frac{180712333845900}{214358881} a + \frac{849035189860568}{214358881} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 32 a^{2} - 28 a - 205\) , \( 129 a^{2} - 104 a - 829\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(32a^{2}-28a-205\right){x}+129a^{2}-104a-829$ |
| 11.2-a4 |
11.2-a |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$3.51820$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$43.94898302$ |
1.664686436 |
\( \frac{12842626367}{14641} a^{2} - \frac{27816708251}{14641} a - \frac{29661435944}{14641} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 2 a^{2} - 3 a - 10\) , \( 2 a^{2} - 2 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(2a^{2}-3a-10\right){x}+2a^{2}-2a-12$ |
| 11.2-b1 |
11.2-b |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$3.51820$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.526854108$ |
$61.17016409$ |
1.831069745 |
\( -\frac{21122737673865178}{14641} a^{2} + \frac{34361275652236931}{14641} a + \frac{173526626002163266}{14641} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( 313 a^{2} - 194 a - 2144\) , \( -5925 a^{2} + 4915 a + 37030\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(313a^{2}-194a-2144\right){x}-5925a^{2}+4915a+37030$ |
| 11.2-b2 |
11.2-b |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{16} \) |
$3.51820$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.107416435$ |
$15.29254102$ |
1.831069745 |
\( -\frac{11805919766521078150}{45949729863572161} a^{2} + \frac{23778098342787800525}{45949729863572161} a + \frac{145448866834889845358}{45949729863572161} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( 43 a^{2} - 54 a - 204\) , \( -5 a^{2} - 79 a + 284\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(43a^{2}-54a-204\right){x}-5a^{2}-79a+284$ |
| 11.2-b3 |
11.2-b |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$3.51820$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.053708217$ |
$122.3403281$ |
1.831069745 |
\( -\frac{97386354175171}{214358881} a^{2} + \frac{180712333845900}{214358881} a + \frac{849035189860568}{214358881} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( 18 a^{2} - 4 a - 134\) , \( -79 a^{2} + 46 a + 559\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(18a^{2}-4a-134\right){x}-79a^{2}+46a+559$ |
| 11.2-b4 |
11.2-b |
$4$ |
$4$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$3.51820$ |
$(a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.526854108$ |
$244.6806563$ |
1.831069745 |
\( \frac{12842626367}{14641} a^{2} - \frac{27816708251}{14641} a - \frac{29661435944}{14641} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( -2 a^{2} + 11 a - 4\) , \( 14 a^{2} - 30 a - 25\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-2a^{2}+11a-4\right){x}+14a^{2}-30a-25$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$71.70969112$ |
1.358099117 |
\( -\frac{667419984072}{289} a^{2} + \frac{523199870823}{289} a + \frac{4264532955487}{289} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( 1\) , \( -6 a^{2} - 27 a - 30\) , \( 75 a^{2} + 61 a - 220\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-6a^{2}-27a-30\right){x}+75a^{2}+61a-220$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$143.4193822$ |
1.358099117 |
\( \frac{65809}{17} a^{2} - \frac{623342}{17} a + \frac{1340721}{17} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( 1\) , \( -6 a^{2} + 3 a + 35\) , \( -4 a^{2} + 3 a + 25\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-6a^{2}+3a+35\right){x}-4a^{2}+3a+25$ |
| 17.1-b1 |
17.1-b |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.724536128$ |
$23.43132633$ |
2.295852801 |
\( -\frac{63221697420751}{83521} a^{2} + \frac{49490981631699}{83521} a + \frac{403809752340760}{83521} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( 4 a^{2} - 8 a - 15\) , \( -5 a^{2} + 13 a + 2\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(4a^{2}-8a-15\right){x}-5a^{2}+13a+2$ |
| 17.1-b2 |
17.1-b |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.862268064$ |
$46.86265267$ |
2.295852801 |
\( \frac{3641328}{289} a^{2} - \frac{3041073}{289} a - \frac{22462370}{289} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( -a^{2} + 2 a\) , \( -a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+2a\right){x}-a^{2}+2a+1$ |
| 17.1-b3 |
17.1-b |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{12} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$5.173608386$ |
$7.810442111$ |
2.295852801 |
\( \frac{90013459819401950447}{582622237229761} a^{2} + \frac{348809792072041317292}{582622237229761} a + \frac{219322610632172591580}{582622237229761} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( -96 a^{2} + 202 a + 210\) , \( -962 a^{2} + 2092 a + 2216\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-96a^{2}+202a+210\right){x}-962a^{2}+2092a+2216$ |
| 17.1-b4 |
17.1-b |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.586804193$ |
$15.62088422$ |
2.295852801 |
\( \frac{131375025799477551}{24137569} a^{2} - \frac{284559987275255811}{24137569} a - \frac{303264657356132840}{24137569} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( -96 a^{2} + 207 a + 220\) , \( -963 a^{2} + 2085 a + 2223\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-96a^{2}+207a+220\right){x}-963a^{2}+2085a+2223$ |
| 17.1-c1 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.596553106$ |
0.967580178 |
\( -\frac{2879249607631771904752}{83521} a^{2} + \frac{2253906630956500517103}{83521} a + \frac{18390386521404518009291}{83521} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( -90 a^{2} + 523 a - 757\) , \( -2736 a^{2} + 10245 a - 6434\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(-90a^{2}+523a-757\right){x}-2736a^{2}+10245a-6434$ |
| 17.1-c2 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{16} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$1.596553106$ |
0.967580178 |
\( \frac{183829318516945518886640}{48661191875666868481} a^{2} - \frac{139992000735298073608751}{48661191875666868481} a - \frac{1185923485111742796546619}{48661191875666868481} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( 23 a - 57\) , \( -84 a^{2} + 253 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(23a-57\right){x}-84a^{2}+253a+4$ |
| 17.1-c3 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$12.77242485$ |
0.967580178 |
\( -\frac{569103945996193663}{6975757441} a^{2} + \frac{444325120833032186}{6975757441} a + \frac{3639142447015499113}{6975757441} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( -5 a^{2} + 33 a - 47\) , \( -36 a^{2} + 143 a - 105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(-5a^{2}+33a-47\right){x}-36a^{2}+143a-105$ |
| 17.1-c4 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$51.08969941$ |
0.967580178 |
\( \frac{1382764996953944349407}{289} a^{2} + \frac{4077536635636398631878}{289} a + \frac{2344600683768746747079}{289} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( 5 a^{2} - 27 a - 37\) , \( -6 a^{2} + 41 a + 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(5a^{2}-27a-37\right){x}-6a^{2}+41a+51$ |
| 17.1-c5 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$102.1793988$ |
0.967580178 |
\( \frac{41816865134957}{83521} a^{2} + \frac{123311925757669}{83521} a + \frac{70906896056773}{83521} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( 3 a - 2\) , \( a^{2} - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(3a-2\right){x}+a^{2}-5$ |
| 17.1-c6 |
17.1-c |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$204.3587976$ |
0.967580178 |
\( \frac{2444330}{289} a^{2} - \frac{12809571}{289} a - \frac{11518861}{289} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 4\) , \( 3 a + 3\) , \( 2 a^{2} - a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(3a+3\right){x}+2a^{2}-a-4$ |
| 17.1-d1 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$11.03814315$ |
1.672397941 |
\( -\frac{2879249607631771904752}{83521} a^{2} + \frac{2253906630956500517103}{83521} a + \frac{18390386521404518009291}{83521} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( 330 a^{2} - 293 a - 2240\) , \( -6054 a^{2} + 4912 a + 38758\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(330a^{2}-293a-2240\right){x}-6054a^{2}+4912a+38758$ |
| 17.1-d2 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$5.519071575$ |
1.672397941 |
\( \frac{1382764996953944349407}{289} a^{2} + \frac{4077536635636398631878}{289} a + \frac{2344600683768746747079}{289} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -105 a^{2} - 328 a - 210\) , \( -1853 a^{2} - 5473 a - 3157\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-105a^{2}-328a-210\right){x}-1853a^{2}-5473a-3157$ |
| 17.1-d3 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$22.07628630$ |
1.672397941 |
\( -\frac{569103945996193663}{6975757441} a^{2} + \frac{444325120833032186}{6975757441} a + \frac{3639142447015499113}{6975757441} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( 15 a^{2} - 38 a - 150\) , \( -135 a^{2} + 11 a + 651\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(15a^{2}-38a-150\right){x}-135a^{2}+11a+651$ |
| 17.1-d4 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{16} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$2.759535787$ |
1.672397941 |
\( \frac{183829318516945518886640}{48661191875666868481} a^{2} - \frac{139992000735298073608751}{48661191875666868481} a - \frac{1185923485111742796546619}{48661191875666868481} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( 20 a^{2} - 23 a - 140\) , \( -184 a^{2} - 126 a + 584\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(20a^{2}-23a-140\right){x}-184a^{2}-126a+584$ |
| 17.1-d5 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$44.15257260$ |
1.672397941 |
\( \frac{41816865134957}{83521} a^{2} + \frac{123311925757669}{83521} a + \frac{70906896056773}{83521} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -5 a^{2} - 23 a - 20\) , \( -28 a^{2} - 75 a - 29\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-5a^{2}-23a-20\right){x}-28a^{2}-75a-29$ |
| 17.1-d6 |
17.1-d |
$6$ |
$8$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$88.30514520$ |
1.672397941 |
\( \frac{2444330}{289} a^{2} - \frac{12809571}{289} a - \frac{11518861}{289} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -3 a\) , \( -2 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}-3a{x}-2a-2$ |
| 17.1-e1 |
17.1-e |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{12} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$10.30317062$ |
$3.817125992$ |
2.234509766 |
\( \frac{90013459819401950447}{582622237229761} a^{2} + \frac{348809792072041317292}{582622237229761} a + \frac{219322610632172591580}{582622237229761} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -35 a^{2} - 96 a - 61\) , \( -345 a^{2} - 982 a - 555\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-35a^{2}-96a-61\right){x}-345a^{2}-982a-555$ |
| 17.1-e2 |
17.1-e |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{4} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$3.434390209$ |
$103.0624017$ |
2.234509766 |
\( -\frac{63221697420751}{83521} a^{2} + \frac{49490981631699}{83521} a + \frac{403809752340760}{83521} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -6 a - 11\) , \( 3 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-6a-11\right){x}+3a+7$ |
| 17.1-e3 |
17.1-e |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.717195104$ |
$206.1248035$ |
2.234509766 |
\( \frac{3641328}{289} a^{2} - \frac{3041073}{289} a - \frac{22462370}{289} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-a-1\right){x}$ |
| 17.1-e4 |
17.1-e |
$4$ |
$6$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$3.78294$ |
$(2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$5.151585314$ |
$7.634251984$ |
2.234509766 |
\( \frac{131375025799477551}{24137569} a^{2} - \frac{284559987275255811}{24137569} a - \frac{303264657356132840}{24137569} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a^{2} - a + 4\) , \( -14 a^{2} - 7 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}-a+4\right){x}-14a^{2}-7a+4$ |
| 17.1-f1 |
17.1-f |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.5839361$ |
1.923882977 |
\( -\frac{667419984072}{289} a^{2} + \frac{523199870823}{289} a + \frac{4264532955487}{289} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( 6 a^{2} - 6 a - 43\) , \( -16 a^{2} + 9 a + 94\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(6a^{2}-6a-43\right){x}-16a^{2}+9a+94$ |
| 17.1-f2 |
17.1-f |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$3.78294$ |
$(2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$203.1678722$ |
1.923882977 |
\( \frac{65809}{17} a^{2} - \frac{623342}{17} a + \frac{1340721}{17} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( a^{2} - a - 8\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(a^{2}-a-8\right){x}-1$ |
| 23.1-a1 |
23.1-a |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$3.97841$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.209680137$ |
$110.8131942$ |
2.640302162 |
\( -\frac{212670}{23} a^{2} + \frac{478001}{23} a + \frac{480840}{23} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 4\) , \( a + 1\) , \( a + 2\) , \( -a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a+2\right){x}-a^{2}+2a+2$ |
| 23.1-b1 |
23.1-b |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$3.97841$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$49.26387972$ |
1.866002504 |
\( -\frac{212670}{23} a^{2} + \frac{478001}{23} a + \frac{480840}{23} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -3 a^{2} - 6 a + 2\) , \( a^{2} - 3 a - 11\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3a^{2}-6a+2\right){x}+a^{2}-3a-11$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$4.03408$ |
$(-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.198787151$ |
$57.76243326$ |
2.609568207 |
\( -\frac{525672}{125} a^{2} + \frac{73021}{25} a + \frac{3267004}{125} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 5\) , \( 3 a^{2} - 2 a - 7\) , \( -a^{2} + 8 a - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(3a^{2}-2a-7\right){x}-a^{2}+8a-4$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$4.03408$ |
$(-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \) |
$0.144897740$ |
$36.67537351$ |
2.415466491 |
\( -\frac{525672}{125} a^{2} + \frac{73021}{25} a + \frac{3267004}{125} \) |
\( \bigl[a^{2} - 5\) , \( -a - 1\) , \( a^{2} - a - 4\) , \( a^{2} - 2 a - 8\) , \( -2\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a^{2}-2a-8\right){x}-2$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$4.08616$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$9$ |
\( 1 \) |
$1$ |
$6.252184426$ |
2.131365348 |
\( \frac{87935620292142571520}{3} a^{2} - \frac{68837382277746970624}{3} a - 187220786639926558720 \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - a - 4\) , \( -39 a^{2} - 117 a - 73\) , \( 971 a^{2} + 2859 a + 1637\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a^{2}-117a-73\right){x}+971a^{2}+2859a+1637$ |
| 27.1-b1 |
27.1-b |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{12} \) |
$4.08616$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$38.54379725$ |
1.459950425 |
\( \frac{4255253209}{81} a^{2} - \frac{9216918962}{81} a - \frac{9822611105}{81} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 6\) , \( 0\) , \( -4 a^{2} - 12 a - 8\) , \( -13 a^{2} - 38 a - 22\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-4a^{2}-12a-8\right){x}-13a^{2}-38a-22$ |
| 27.1-b2 |
27.1-b |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{6} \) |
$4.08616$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$77.08759450$ |
1.459950425 |
\( \frac{7787}{3} a^{2} - \frac{51547}{9} a - \frac{40955}{9} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 6\) , \( 0\) , \( a^{2} + 3 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(a^{2}+3a+2\right){x}$ |
| 27.1-c1 |
27.1-c |
$1$ |
$1$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$4.08616$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$41.78855116$ |
1.582854244 |
\( \frac{87935620292142571520}{3} a^{2} - \frac{68837382277746970624}{3} a - 187220786639926558720 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 5\) , \( -16 a^{2} + 27 a + 30\) , \( 68 a^{2} - 181 a - 183\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-16a^{2}+27a+30\right){x}+68a^{2}-181a-183$ |
| 27.1-d1 |
27.1-d |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{6} \) |
$4.08616$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$100.2397520$ |
1.898425676 |
\( \frac{7787}{3} a^{2} - \frac{51547}{9} a - \frac{40955}{9} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a + 1\) , \( 3 a + 5\) , \( a^{2} + 3 a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(3a+5\right){x}+a^{2}+3a+1$ |
| 27.1-d2 |
27.1-d |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{12} \) |
$4.08616$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$50.11987604$ |
1.898425676 |
\( \frac{4255253209}{81} a^{2} - \frac{9216918962}{81} a - \frac{9822611105}{81} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a + 1\) , \( -5 a^{2} + 13 a + 15\) , \( -10 a^{2} + 24 a + 25\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-5a^{2}+13a+15\right){x}-10a^{2}+24a+25$ |
| 37.1-a1 |
37.1-a |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{4} \) |
$4.30647$ |
$(a^2-2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.447576966$ |
$118.4143923$ |
3.011251917 |
\( -\frac{847184617593}{1874161} a^{2} + \frac{745877389554}{1874161} a + \frac{5593446939393}{1874161} \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 4\) , \( -27 a^{2} - 78 a - 37\) , \( 228 a^{2} + 675 a + 391\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-27a^{2}-78a-37\right){x}+228a^{2}+675a+391$ |
| 37.1-a2 |
37.1-a |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$4.30647$ |
$(a^2-2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.223788483$ |
$236.8287846$ |
3.011251917 |
\( \frac{578097}{1369} a^{2} - \frac{935307}{1369} a - \frac{2348811}{1369} \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 4\) , \( -2 a^{2} - 3 a + 8\) , \( 6 a^{2} + 22 a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-2a^{2}-3a+8\right){x}+6a^{2}+22a+18$ |
| 37.1-b1 |
37.1-b |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{4} \) |
$4.30647$ |
$(a^2-2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.725888381$ |
$25.80900017$ |
2.530805418 |
\( -\frac{847184617593}{1874161} a^{2} + \frac{745877389554}{1874161} a + \frac{5593446939393}{1874161} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( 0\) , \( -4 a - 4\) , \( -3 a^{2} - 9 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+a{x}^{2}+\left(-4a-4\right){x}-3a^{2}-9a-6$ |
| 37.1-b2 |
37.1-b |
$2$ |
$2$ |
3.3.697.1 |
$3$ |
$[3, 0]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$4.30647$ |
$(a^2-2a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.862944190$ |
$51.61800035$ |
2.530805418 |
\( \frac{578097}{1369} a^{2} - \frac{935307}{1369} a - \frac{2348811}{1369} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( 0\) , \( a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+a{x}^{2}+\left(a+1\right){x}$ |
*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.
