| 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 |
| 7.1-a1 |
7.1-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{18} \) |
$2.34824$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.204444745$ |
0.995789544 |
\( \frac{106799246379653196265}{1628413597910449} a^{2} - \frac{444440110858767442406}{1628413597910449} a + \frac{386900295055167754239}{1628413597910449} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -30 a^{2} + 89 a - 71\) , \( -244 a^{2} + 801 a - 616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-30a^{2}+89a-71\right){x}-244a^{2}+801a-616$ |
| 7.1-a2 |
7.1-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{6} \) |
$2.34824$ |
$(-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$113.5200081$ |
0.995789544 |
\( -\frac{37425200478480}{117649} a^{2} - \frac{8303854626841}{117649} a + \frac{214405413963731}{117649} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 11\) , \( a^{2} - 5 a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-11\right){x}+a^{2}-5a+5$ |
| 7.1-a3 |
7.1-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$2.34824$ |
$(-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$227.0400162$ |
0.995789544 |
\( -\frac{2982457}{343} a^{2} - \frac{539306}{343} a + \frac{17550111}{343} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}-a$ |
| 7.1-a4 |
7.1-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{9} \) |
$2.34824$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.408889490$ |
0.995789544 |
\( \frac{15576798628679483}{40353607} a^{2} + \frac{20019297620439013}{40353607} a - \frac{47713669240844510}{40353607} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a^{2} - a + 4\) , \( -16 a^{2} + 4 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a^{2}-a+4\right){x}-16a^{2}+4a+15$ |
| 7.2-a1 |
7.2-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{18} \) |
$2.34824$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.204444745$ |
0.995789544 |
\( -\frac{551239357238420638671}{1628413597910449} a^{2} - \frac{106799246379653196265}{1628413597910449} a + \frac{446550565129588041464}{232630513987207} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a^{2} - 3\) , \( 119 a^{2} + 30 a - 697\) , \( 1045 a^{2} + 244 a - 6016\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(119a^{2}+30a-697\right){x}+1045a^{2}+244a-6016$ |
| 7.2-a2 |
7.2-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{9} \) |
$2.34824$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.408889490$ |
0.995789544 |
\( \frac{4442498991759530}{40353607} a^{2} - \frac{15576798628679483}{40353607} a + \frac{1771475419359255}{5764801} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a^{2} - 3\) , \( 4 a^{2} + 5 a - 37\) , \( 20 a^{2} + 16 a - 145\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(4a^{2}+5a-37\right){x}+20a^{2}+16a-145$ |
| 7.2-a3 |
7.2-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{6} \) |
$2.34824$ |
$(-a^2+4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$113.5200081$ |
0.995789544 |
\( \frac{29121345851639}{117649} a^{2} + \frac{37425200478480}{117649} a - \frac{12743710262175}{16807} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a^{2} - 3\) , \( 4 a^{2} - 27\) , \( -6 a^{2} - a + 34\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(4a^{2}-27\right){x}-6a^{2}-a+34$ |
| 7.2-a4 |
7.2-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$2.34824$ |
$(-a^2+4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$227.0400162$ |
0.995789544 |
\( \frac{2443151}{343} a^{2} + \frac{2982457}{343} a - \frac{1019254}{49} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a^{2} - 3\) , \( -a^{2} + 3\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}-a^{2}+4$ |
| 7.3-a1 |
7.3-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{9} \) |
$2.34824$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.408889490$ |
0.995789544 |
\( -\frac{20019297620439013}{40353607} a^{2} - \frac{4442498991759530}{40353607} a + \frac{16384287625152641}{5764801} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 4\) , \( -a^{2} - 6 a - 11\) , \( -5 a^{2} - 21 a - 24\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-a^{2}-6a-11\right){x}-5a^{2}-21a-24$ |
| 7.3-a2 |
7.3-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{3} \) |
$2.34824$ |
$(a^2+a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$227.0400162$ |
0.995789544 |
\( \frac{539306}{343} a^{2} - \frac{2443151}{343} a + \frac{417679}{49} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 4\) , \( -a^{2} - a + 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-a^{2}-a+4\right){x}$ |
| 7.3-a3 |
7.3-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{6} \) |
$2.34824$ |
$(a^2+a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$113.5200081$ |
0.995789544 |
\( \frac{8303854626841}{117649} a^{2} - \frac{29121345851639}{117649} a + \frac{3312191273658}{16807} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 4\) , \( -6 a^{2} - 6 a + 19\) , \( 4 a^{2} + 5 a - 11\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-6a^{2}-6a+19\right){x}+4a^{2}+5a-11$ |
| 7.3-a4 |
7.3-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{18} \) |
$2.34824$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.204444745$ |
0.995789544 |
\( \frac{444440110858767442406}{1628413597910449} a^{2} + \frac{551239357238420638671}{1628413597910449} a - \frac{201157610531436667533}{232630513987207} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 4\) , \( -91 a^{2} - 121 a + 264\) , \( -802 a^{2} - 1046 a + 2418\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-91a^{2}-121a+264\right){x}-802a^{2}-1046a+2418$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{27} \) |
$2.40108$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.439208585$ |
$1.978737580$ |
1.074519674 |
\( -\frac{246579625}{512} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( 1\) , \( 24 a^{2} - 6 a - 163\) , \( 157 a^{2} + 5 a - 975\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(24a^{2}-6a-163\right){x}+157a^{2}+5a-975$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$2.40108$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.146402861$ |
$53.42591466$ |
1.074519674 |
\( \frac{2375}{8} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( 1\) , \( -a^{2} - a + 7\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}-a+7\right){x}-1$ |
| 11.1-a1 |
11.1-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$2.53196$ |
$(a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.533083138$ |
$135.1260038$ |
1.263743758 |
\( \frac{15157070}{1331} a^{2} + \frac{3336499}{1331} a - \frac{87193995}{1331} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( 5 a^{2} + 3 a - 24\) , \( -6 a^{2} + a + 40\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(5a^{2}+3a-24\right){x}-6a^{2}+a+40$ |
| 11.1-a2 |
11.1-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{9} \) |
$2.53196$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.599249416$ |
$5.004666807$ |
1.263743758 |
\( -\frac{52375204213316035}{2357947691} a^{2} + \frac{183678451295599417}{2357947691} a - \frac{146233942238531042}{2357947691} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( -15 a^{2} + 3 a + 81\) , \( -12 a^{2} + 6 a + 61\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-15a^{2}+3a+81\right){x}-12a^{2}+6a+61$ |
| 11.2-a1 |
11.2-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{3} \) |
$2.53196$ |
$(-a^2-a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.533083138$ |
$135.1260038$ |
1.263743758 |
\( -\frac{3336499}{1331} a^{2} + \frac{11820571}{1331} a - \frac{9883220}{1331} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 3\) , \( 4 a^{2} - a - 28\) , \( -27 a^{2} - 7 a + 152\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(4a^{2}-a-28\right){x}-27a^{2}-7a+152$ |
| 11.2-a2 |
11.2-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{9} \) |
$2.53196$ |
$(-a^2-a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.599249416$ |
$5.004666807$ |
1.263743758 |
\( -\frac{183678451295599417}{2357947691} a^{2} - \frac{236053655508915452}{2357947691} a + \frac{562657497386201903}{2357947691} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 3\) , \( -56 a^{2} - 16 a + 312\) , \( 638 a^{2} + 138 a - 3664\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-56a^{2}-16a+312\right){x}+638a^{2}+138a-3664$ |
| 11.3-a1 |
11.3-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( - 11^{9} \) |
$2.53196$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.599249416$ |
$5.004666807$ |
1.263743758 |
\( \frac{236053655508915452}{2357947691} a^{2} + \frac{52375204213316035}{2357947691} a - \frac{1352324585340773025}{2357947691} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 797 a^{2} + 177 a - 4564\) , \( 17501 a^{2} + 3884 a - 100260\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(797a^{2}+177a-4564\right){x}+17501a^{2}+3884a-100260$ |
| 11.3-a2 |
11.3-a |
$2$ |
$3$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( - 11^{3} \) |
$2.53196$ |
$(a^2-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.533083138$ |
$135.1260038$ |
1.263743758 |
\( -\frac{11820571}{1331} a^{2} - \frac{15157070}{1331} a + \frac{35873639}{1331} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 7 a^{2} + 2 a - 39\) , \( 42 a^{2} + 10 a - 239\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(7a^{2}+2a-39\right){x}+42a^{2}+10a-239$ |
| 19.1-a1 |
19.1-a |
$3$ |
$9$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$2.77343$ |
$(a^2-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 3 \) |
$1$ |
$0.093115668$ |
1.190900389 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$ |
| 19.1-a2 |
19.1-a |
$3$ |
$9$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{9} \) |
$2.77343$ |
$(a^2-a-4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 3^{2} \) |
$1$ |
$2.514123044$ |
1.190900389 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$ |
| 19.1-a3 |
19.1-a |
$3$ |
$9$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$2.77343$ |
$(a^2-a-4)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3 \) |
$1$ |
$67.88132220$ |
1.190900389 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+{x}$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$2.94071$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$26.97792726$ |
1.419890908 |
\( -\frac{16680546304}{3} a^{2} + \frac{58498789376}{3} a - \frac{46574526464}{3} \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( a + 1\) , \( -6 a^{2} + 6 a + 18\) , \( -7 a^{2} + 10 a + 11\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}+6a+18\right){x}-7a^{2}+10a+11$ |
| 27.1-b1 |
27.1-b |
$2$ |
$7$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{21} \) |
$2.94071$ |
$(3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 1 \) |
$24.99860541$ |
$0.453772509$ |
1.791107353 |
\( -\frac{89289015625}{2187} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( 173 a^{2} - 36 a - 1178\) , \( 2645 a^{2} + 70 a - 16452\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(173a^{2}-36a-1178\right){x}+2645a^{2}+70a-16452$ |
| 27.1-b2 |
27.1-b |
$2$ |
$7$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$2.94071$ |
$(3)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$3.571229344$ |
$155.6439706$ |
1.791107353 |
\( \frac{2375}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -2 a^{2} - a + 12\) , \( -a^{2} + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-2a^{2}-a+12\right){x}-a^{2}+5$ |
| 27.1-c1 |
27.1-c |
$1$ |
$1$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$2.94071$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$26.97792726$ |
1.419890908 |
\( -\frac{58498789376}{3} a^{2} - 25059778560 a + \frac{179197235200}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 10 a^{2} - 62\) , \( -31 a^{2} - 14 a + 159\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a^{2}-62\right){x}-31a^{2}-14a+159$ |
| 27.1-d1 |
27.1-d |
$1$ |
$1$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$2.94071$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$26.97792726$ |
1.419890908 |
\( 25059778560 a^{2} + \frac{16680546304}{3} a - \frac{430694600704}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( a^{2} + a - 3\) , \( 7 a^{2} + 14 a - 26\) , \( 11 a^{2} + 4 a - 21\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a^{2}+14a-26\right){x}+11a^{2}+4a-21$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{6} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.40792394$ |
1.705680207 |
\( \frac{110016776831}{2401} a^{2} - \frac{386002347110}{2401} a + \frac{43939502864}{343} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( a + 1\) , \( 37 a^{2} + 8 a - 210\) , \( -152 a^{2} - 39 a + 857\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(37a^{2}+8a-210\right){x}-152a^{2}-39a+857$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$64.81584789$ |
1.705680207 |
\( \frac{45431}{49} a^{2} + \frac{451959}{49} a - 10587 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( a + 1\) , \( 2 a^{2} - 2 a - 15\) , \( 5 a^{2} - 32\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(2a^{2}-2a-15\right){x}+5a^{2}-32$ |
| 49.1-b1 |
49.1-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{8} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.567098078$ |
$8.115035790$ |
2.007956368 |
\( -\frac{1799399156778628}{2401} a^{2} - \frac{399243780606817}{2401} a + \frac{10308568484762263}{2401} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( 25 a^{2} - 9 a - 167\) , \( 91 a^{2} - 41 a - 665\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(25a^{2}-9a-167\right){x}+91a^{2}-41a-665$ |
| 49.1-b2 |
49.1-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$129.8405726$ |
2.007956368 |
\( \frac{4439}{7} a^{2} + \frac{4733}{7} a - \frac{17358}{7} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( -4 a + 3\) , \( -3 a + 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-4a+3\right){x}-3a+3$ |
| 49.1-b3 |
49.1-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.783549039$ |
$64.92028632$ |
2.007956368 |
\( \frac{196615}{7} a^{2} + \frac{18153570}{49} a + \frac{60264873}{49} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( -10 a^{2} - 19 a + 28\) , \( -40 a^{2} - 56 a + 121\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-10a^{2}-19a+28\right){x}-40a^{2}-56a+121$ |
| 49.1-b4 |
49.1-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a), (-a^2+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$32.46014316$ |
2.007956368 |
\( \frac{6874535884572}{7} a^{2} + \frac{8407840587271}{7} a - \frac{20536893880337}{7} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( -205 a^{2} - 269 a + 623\) , \( -2631 a^{2} - 3383 a + 8059\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-205a^{2}-269a+623\right){x}-2631a^{2}-3383a+8059$ |
| 49.2-a1 |
49.2-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{3} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$64.81584789$ |
1.705680207 |
\( -\frac{451959}{49} a^{2} - \frac{406528}{49} a + \frac{1922756}{49} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( 4 a^{2} + a - 21\) , \( 3 a^{2} + a - 16\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(4a^{2}+a-21\right){x}+3a^{2}+a-16$ |
| 49.2-a2 |
49.2-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{6} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.40792394$ |
1.705680207 |
\( \frac{386002347110}{2401} a^{2} + \frac{496019123941}{2401} a - \frac{1182368108178}{2401} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( -6 a^{2} - 4 a + 29\) , \( 18 a^{2} - 6 a - 128\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-6a^{2}-4a+29\right){x}+18a^{2}-6a-128$ |
| 49.2-b1 |
49.2-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$32.46014316$ |
2.007956368 |
\( -\frac{8407840587271}{7} a^{2} - 219043528957 a + \frac{49000452594306}{7} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 265 a^{2} + 56 a - 1521\) , \( 3054 a^{2} + 681 a - 17506\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(265a^{2}+56a-1521\right){x}+3054a^{2}+681a-17506$ |
| 49.2-b2 |
49.2-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.567098078$ |
$8.115035790$ |
2.007956368 |
\( \frac{399243780606817}{2401} a^{2} - \frac{200022196595973}{343} a + \frac{1114752954613666}{2401} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 5 a^{2} + 26 a - 91\) , \( 2 a^{2} + 191 a - 452\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(5a^{2}+26a-91\right){x}+2a^{2}+191a-452$ |
| 49.2-b3 |
49.2-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{4} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.783549039$ |
$64.92028632$ |
2.007956368 |
\( -\frac{18153570}{49} a^{2} - \frac{16777265}{49} a + \frac{156537943}{49} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 15 a^{2} + a - 86\) , \( 32 a^{2} + 10 a - 195\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(15a^{2}+a-86\right){x}+32a^{2}+10a-195$ |
| 49.2-b4 |
49.2-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a), (a^2+a-5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$129.8405726$ |
2.007956368 |
\( -\frac{4733}{7} a^{2} - 42 a + \frac{24063}{7} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( -4 a + 4\) , \( -a^{2} - 3 a + 7\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-4a+4\right){x}-a^{2}-3a+7$ |
| 49.3-a1 |
49.3-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{6} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.40792394$ |
1.705680207 |
\( -\frac{496019123941}{2401} a^{2} - \frac{110016776831}{2401} a + \frac{405962414281}{343} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( 2 a^{2} - 2 a - 5\) , \( 5 a^{2} + 24 a - 81\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(2a^{2}-2a-5\right){x}+5a^{2}+24a-81$ |
| 49.3-a2 |
49.3-a |
$2$ |
$2$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{3} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$64.81584789$ |
1.705680207 |
\( \frac{406528}{49} a^{2} - \frac{45431}{49} a - \frac{273960}{7} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( -3 a^{2} + 3 a + 10\) , \( -2 a^{2} + 2 a + 6\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-3a^{2}+3a+10\right){x}-2a^{2}+2a+6$ |
| 49.3-b1 |
49.3-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$32.46014316$ |
2.007956368 |
\( 219043528957 a^{2} - \frac{6874535884572}{7} a + 1100366675961 \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{2} - 4\) , \( -58 a^{2} + 208 a - 172\) , \( -682 a^{2} + 2373 a - 1880\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-58a^{2}+208a-172\right){x}-682a^{2}+2373a-1880$ |
| 49.3-b2 |
49.3-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{4} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.783549039$ |
$64.92028632$ |
2.007956368 |
\( \frac{16777265}{49} a^{2} - \frac{196615}{7} a + 762 \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{2} - 4\) , \( -3 a^{2} + 13 a - 12\) , \( -11 a^{2} + 22 a - 12\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{2}+13a-12\right){x}-11a^{2}+22a-12$ |
| 49.3-b3 |
49.3-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.567098078$ |
$129.8405726$ |
2.007956368 |
\( 42 a^{2} - \frac{4439}{7} a + 523 \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{2} - 4\) , \( 2 a^{2} + 3 a - 7\) , \( 2 a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a^{2}+3a-7\right){x}+2a^{2}+2a-7$ |
| 49.3-b4 |
49.3-b |
$4$ |
$4$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{8} \) |
$3.24782$ |
$(-a^2+4), (a^2+a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.567098078$ |
$8.115035790$ |
2.007956368 |
\( \frac{200022196595973}{343} a^{2} + \frac{1799399156778628}{2401} a - \frac{612721257688303}{343} \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{2} - 4\) , \( -28 a^{2} - 22 a + 68\) , \( -192 a^{2} - 189 a + 516\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-28a^{2}-22a+68\right){x}-192a^{2}-189a+516$ |
| 49.4-a1 |
49.4-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.4 |
\( 7^{2} \) |
\( - 7^{15} \) |
$3.24782$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$7.133888584$ |
1.689605191 |
\( -\frac{20019297620439013}{40353607} a^{2} - \frac{4442498991759530}{40353607} a + \frac{16384287625152641}{5764801} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( -3 a^{2} - 34 a - 58\) , \( 362 a^{2} + 387 a - 1311\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-3a^{2}-34a-58\right){x}+362a^{2}+387a-1311$ |
| 49.4-a2 |
49.4-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.4 |
\( 7^{2} \) |
\( - 7^{9} \) |
$3.24782$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$64.20499726$ |
1.689605191 |
\( \frac{539306}{343} a^{2} - \frac{2443151}{343} a + \frac{417679}{49} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( 2 a^{2} + a + 2\) , \( -8 a^{2} - 12 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(2a^{2}+a+2\right){x}-8a^{2}-12a+24$ |
| 49.4-a3 |
49.4-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.4 |
\( 7^{2} \) |
\( - 7^{12} \) |
$3.24782$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.10249863$ |
1.689605191 |
\( \frac{8303854626841}{117649} a^{2} - \frac{29121345851639}{117649} a + \frac{3312191273658}{16807} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( -28 a^{2} - 34 a + 97\) , \( -77 a^{2} - 103 a + 225\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-28a^{2}-34a+97\right){x}-77a^{2}-103a+225$ |
| 49.4-a4 |
49.4-a |
$4$ |
$6$ |
3.3.361.1 |
$3$ |
$[3, 0]$ |
49.4 |
\( 7^{2} \) |
\( - 7^{24} \) |
$3.24782$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$3.566944292$ |
1.689605191 |
\( \frac{444440110858767442406}{1628413597910449} a^{2} + \frac{551239357238420638671}{1628413597910449} a - \frac{201157610531436667533}{232630513987207} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( -568 a^{2} - 759 a + 1672\) , \( 12800 a^{2} + 16370 a - 39416\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-568a^{2}-759a+1672\right){x}+12800a^{2}+16370a-39416$ |
*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.
