| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.06607$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$31.43077920$ |
0.980299069 |
\( \frac{17690975205668}{9} a^{2} + \frac{20899317547511}{9} a - \frac{7973191675235}{3} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -116 a^{2} + 341 a - 191\) , \( 1561 a^{2} - 4537 a + 2428\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-116a^{2}+341a-191\right){x}+1561a^{2}-4537a+2428$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{16} \) |
$2.06607$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.857694801$ |
0.980299069 |
\( -\frac{637339485144964}{6561} a^{2} + \frac{182573580343201}{6561} a + \frac{893210373928667}{2187} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( 24 a^{2} + 21 a - 161\) , \( 195 a^{2} - 45 a - 846\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(24a^{2}+21a-161\right){x}+195a^{2}-45a-846$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$2.06607$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$62.86155840$ |
0.980299069 |
\( \frac{35323985}{81} a^{2} + \frac{17367094}{27} a - 64775 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -6 a^{2} + 21 a - 16\) , \( 26 a^{2} - 65 a + 15\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-6a^{2}+21a-16\right){x}+26a^{2}-65a+15$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.06607$ |
$(-a^2+a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$125.7231168$ |
0.980299069 |
\( \frac{4519}{9} a^{2} + \frac{4861}{9} a - \frac{2698}{3} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -a^{2} + a + 4\) , \( -2 a + 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+4\right){x}-2a+2$ |
| 9.1-b1 |
9.1-b |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.06607$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.119566432$ |
$8.307343432$ |
0.870235370 |
\( \frac{17690975205668}{9} a^{2} + \frac{20899317547511}{9} a - \frac{7973191675235}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -998 a^{2} + 2900 a - 1562\) , \( -39467 a^{2} + 114933 a - 61916\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-998a^{2}+2900a-1562\right){x}-39467a^{2}+114933a-61916$ |
| 9.1-b2 |
9.1-b |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{16} \) |
$2.06607$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.279891608$ |
$33.22937372$ |
0.870235370 |
\( -\frac{637339485144964}{6561} a^{2} + \frac{182573580343201}{6561} a + \frac{893210373928667}{2187} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -88 a^{2} + 260 a - 152\) , \( 13 a^{2} - 45 a + 32\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-88a^{2}+260a-152\right){x}+13a^{2}-45a+32$ |
| 9.1-b3 |
9.1-b |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$2.06607$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.559783216$ |
$66.45874745$ |
0.870235370 |
\( \frac{35323985}{81} a^{2} + \frac{17367094}{27} a - 64775 \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -63 a^{2} + 180 a - 97\) , \( -601 a^{2} + 1748 a - 942\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-63a^{2}+180a-97\right){x}-601a^{2}+1748a-942$ |
| 9.1-b4 |
9.1-b |
$4$ |
$4$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.06607$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.279891608$ |
$132.9174949$ |
0.870235370 |
\( \frac{4519}{9} a^{2} + \frac{4861}{9} a - \frac{2698}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( -3 a^{2} + 5 a - 2\) , \( -18 a^{2} + 50 a - 27\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-3a^{2}+5a-2\right){x}-18a^{2}+50a-27$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{30} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.26036525$ |
0.951915430 |
\( -\frac{169564940890516}{282429536481} a^{2} - \frac{93767995435637}{282429536481} a + \frac{1032142453154629}{282429536481} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 2 a^{2} + 2 a - 6\) , \( -8 a^{2} - 11 a + 9\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(2a^{2}+2a-6\right){x}-8a^{2}-11a+9$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$30.52073051$ |
0.951915430 |
\( \frac{1812669625}{531441} a^{2} + \frac{2069390414}{531441} a - \frac{1917539791}{531441} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( -3 a^{2} - 3 a + 9\) , \( -7 a^{2} - 6 a + 12\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-3a^{2}-3a+9\right){x}-7a^{2}-6a+12$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.26036525$ |
0.951915430 |
\( \frac{952377494237}{6561} a^{2} - \frac{2793434061809}{6561} a + \frac{1537874453914}{6561} \) |
\( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( 29 a^{2} - 9 a - 123\) , \( 148 a^{2} - 17 a - 575\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(29a^{2}-9a-123\right){x}+148a^{2}-17a-575$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$30.52073051$ |
0.951915430 |
\( \frac{1737352}{81} a^{2} + \frac{3240461}{81} a - \frac{3315481}{81} \) |
\( \bigl[1\) , \( -a^{2} - a + 2\) , \( a\) , \( -a^{2} - 4 a - 3\) , \( 15 a^{2} + 14 a - 29\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-a^{2}-4a-3\right){x}+15a^{2}+14a-29$ |
| 9.2-b1 |
9.2-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{30} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$13.93653059$ |
0.869336893 |
\( -\frac{169564940890516}{282429536481} a^{2} - \frac{93767995435637}{282429536481} a + \frac{1032142453154629}{282429536481} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} + 14 a - 9\) , \( -18 a^{2} - 32 a + 31\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}+14a-9\right){x}-18a^{2}-32a+31$ |
| 9.2-b2 |
9.2-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{18} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$27.87306118$ |
0.869336893 |
\( \frac{1812669625}{531441} a^{2} + \frac{2069390414}{531441} a - \frac{1917539791}{531441} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} - 6 a + 6\) , \( -a^{2} - 5 a + 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}-6a+6\right){x}-a^{2}-5a+4$ |
| 9.2-b3 |
9.2-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$125.4287753$ |
0.869336893 |
\( \frac{952377494237}{6561} a^{2} - \frac{2793434061809}{6561} a + \frac{1537874453914}{6561} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( 4 a^{2} + 4 a - 12\) , \( 21 a^{2} + 28 a - 12\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(4a^{2}+4a-12\right){x}+21a^{2}+28a-12$ |
| 9.2-b4 |
9.2-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$2.06607$ |
$(a^2-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$250.8575506$ |
0.869336893 |
\( \frac{1737352}{81} a^{2} + \frac{3240461}{81} a - \frac{3315481}{81} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( -a^{2} - a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}-a+3\right){x}$ |
| 15.1-a1 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.884794823$ |
0.940562166 |
\( \frac{4561952344347894508816}{50625} a^{2} + \frac{5468372973632837498513}{50625} a - \frac{6224545788789433223542}{50625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -80 a^{2} - 340 a - 369\) , \( -2244 a^{2} - 5118 a - 1584\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-80a^{2}-340a-369\right){x}-2244a^{2}-5118a-1584$ |
| 15.1-a2 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$60.31343436$ |
0.940562166 |
\( \frac{25393788989964280607}{225} a^{2} - \frac{73952533248919150724}{225} a + \frac{39839035941583441516}{225} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a^{2} + 20 a - 64\) , \( -2 a^{2} - 91 a + 193\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{2}+20a-64\right){x}-2a^{2}-91a+193$ |
| 15.1-a3 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$15.07835859$ |
0.940562166 |
\( \frac{311251219371829121}{2562890625} a^{2} + \frac{373240221797370628}{2562890625} a - \frac{424319657035623452}{2562890625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a^{2} - 20 a - 24\) , \( -44 a^{2} - 93 a - 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{2}-20a-24\right){x}-44a^{2}-93a-9$ |
| 15.1-a4 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$120.6268687$ |
0.940562166 |
\( \frac{5176756484309}{50625} a^{2} - \frac{15075007347263}{50625} a + \frac{8121003692917}{50625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -a^{2} - 4 a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4{x}-a^{2}-4a+4$ |
| 15.1-a5 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{16} \cdot 5^{16} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.884794823$ |
0.940562166 |
\( -\frac{28443849277171190300944}{6568408355712890625} a^{2} - \frac{34194402733320830270417}{6568408355712890625} a + \frac{38637799905139432891078}{6568408355712890625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a^{2} - 20 a + 1\) , \( -16 a^{2} - 104 a - 126\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a^{2}-20a+1\right){x}-16a^{2}-104a-126$ |
| 15.1-a6 |
15.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$241.2537374$ |
0.940562166 |
\( -\frac{660182}{225} a^{2} + \frac{2137499}{225} a - \frac{807616}{225} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
| 15.1-b1 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.387233228$ |
1.094672359 |
\( \frac{25393788989964280607}{225} a^{2} - \frac{73952533248919150724}{225} a + \frac{39839035941583441516}{225} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -66 a^{2} + 195 a - 107\) , \( -762 a^{2} + 2197 a - 1180\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-66a^{2}+195a-107\right){x}-762a^{2}+2197a-1180$ |
| 15.1-b2 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$35.09786582$ |
1.094672359 |
\( \frac{5176756484309}{50625} a^{2} - \frac{15075007347263}{50625} a + \frac{8121003692917}{50625} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -6 a^{2} + 10 a - 2\) , \( -16 a^{2} + 41 a - 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-6a^{2}+10a-2\right){x}-16a^{2}+41a-22$ |
| 15.1-b3 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.19573165$ |
1.094672359 |
\( -\frac{660182}{225} a^{2} + \frac{2137499}{225} a - \frac{807616}{225} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -a^{2} + 3\) , \( a - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{2}+3\right){x}+a-2$ |
| 15.1-b4 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$17.54893291$ |
1.094672359 |
\( \frac{311251219371829121}{2562890625} a^{2} + \frac{373240221797370628}{2562890625} a - \frac{424319657035623452}{2562890625} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -26 a^{2} - 15 a + 23\) , \( -114 a^{2} - 75 a + 116\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-26a^{2}-15a+23\right){x}-114a^{2}-75a+116$ |
| 15.1-b5 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{16} \cdot 5^{16} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.193616614$ |
1.094672359 |
\( -\frac{28443849277171190300944}{6568408355712890625} a^{2} - \frac{34194402733320830270417}{6568408355712890625} a + \frac{38637799905139432891078}{6568408355712890625} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -21 a^{2} - 30 a + 33\) , \( -136 a^{2} - 19 a + 88\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-21a^{2}-30a+33\right){x}-136a^{2}-19a+88$ |
| 15.1-b6 |
15.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$2.24968$ |
$(a^2-3), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.774466456$ |
1.094672359 |
\( \frac{4561952344347894508816}{50625} a^{2} + \frac{5468372973632837498513}{50625} a - \frac{6224545788789433223542}{50625} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 1\) , \( -351 a^{2} - 400 a + 413\) , \( -6364 a^{2} - 7615 a + 8876\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-351a^{2}-400a+413\right){x}-6364a^{2}-7615a+8876$ |
| 19.1-a1 |
19.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{12} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$7.793500282$ |
1.458435572 |
\( \frac{33777701165536011237}{2213314919066161} a^{2} - \frac{277355301401585077884}{2213314919066161} a + \frac{184960608190583522339}{2213314919066161} \) |
\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - a - 116\) , \( 36 a^{2} - 32 a - 143\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{2}-a-116\right){x}+36a^{2}-32a-143$ |
| 19.1-a2 |
19.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.38050084$ |
1.458435572 |
\( -\frac{28175458029840}{130321} a^{2} + \frac{8070882399369}{130321} a + \frac{118461749726429}{130321} \) |
\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - 6 a - 91\) , \( 79 a^{2} - 21 a - 332\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{2}-6a-91\right){x}+79a^{2}-21a-332$ |
| 19.1-a3 |
19.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$46.76100169$ |
1.458435572 |
\( \frac{2816089}{361} a^{2} - \frac{532982}{361} a - \frac{11269471}{361} \) |
\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 2 a^{2} - a - 6\) , \( 2 a^{2} - 7\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{2}-a-6\right){x}+2a^{2}-7$ |
| 19.1-a4 |
19.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$15.58700056$ |
1.458435572 |
\( \frac{108976900762638027}{47045881} a^{2} + \frac{130629686944915561}{47045881} a - \frac{148693269376177306}{47045881} \) |
\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( -8 a^{2} - a + 29\) , \( -3 a^{2} - 9 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a^{2}-a+29\right){x}-3a^{2}-9a-5$ |
| 19.1-b1 |
19.1-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{12} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.157201887$ |
0.777957386 |
\( \frac{33777701165536011237}{2213314919066161} a^{2} - \frac{277355301401585077884}{2213314919066161} a + \frac{184960608190583522339}{2213314919066161} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -30 a^{2} + 79 a - 51\) , \( -206 a^{2} + 565 a - 298\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-30a^{2}+79a-51\right){x}-206a^{2}+565a-298$ |
| 19.1-b2 |
19.1-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$112.2444509$ |
0.777957386 |
\( -\frac{28175458029840}{130321} a^{2} + \frac{8070882399369}{130321} a + \frac{118461749726429}{130321} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 11\) , \( a^{2} - 7 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-11\right){x}+a^{2}-7a+9$ |
| 19.1-b3 |
19.1-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$224.4889018$ |
0.777957386 |
\( \frac{2816089}{361} a^{2} - \frac{532982}{361} a - \frac{11269471}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}-a$ |
| 19.1-b4 |
19.1-b |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.34008$ |
$(a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$8.314403774$ |
0.777957386 |
\( \frac{108976900762638027}{47045881} a^{2} + \frac{130629686944915561}{47045881} a - \frac{148693269376177306}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a^{2} - a + 4\) , \( -14 a^{2} + 6 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a^{2}-a+4\right){x}-14a^{2}+6a+3$ |
| 21.1-a1 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{16} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$8.362730790$ |
1.043305628 |
\( -\frac{7508368686128970279577}{299096375126409} a^{2} + \frac{1616589880731750120535}{299096375126409} a + \frac{32458428323711052321331}{299096375126409} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -160 a^{2} + 399 a - 230\) , \( 2052 a^{2} - 6371 a + 3573\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-160a^{2}+399a-230\right){x}+2052a^{2}-6371a+3573$ |
| 21.1-a2 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{16} \cdot 7^{2} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.181365395$ |
1.043305628 |
\( \frac{95456569237420574}{2109289329} a^{2} - \frac{317812138936041299}{2109289329} a + \frac{237309629218867696}{2109289329} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -60 a^{2} + 174 a - 100\) , \( -630 a^{2} + 1828 a - 986\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-60a^{2}+174a-100\right){x}-630a^{2}+1828a-986$ |
| 21.1-a3 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$33.45092316$ |
1.043305628 |
\( \frac{2469125117705}{15752961} a^{2} + \frac{2848919682052}{15752961} a - \frac{3194204179760}{15752961} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -5 a^{2} + 9 a - 5\) , \( -12 a^{2} + 31 a - 18\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-5a^{2}+9a-5\right){x}-12a^{2}+31a-18$ |
| 21.1-a4 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$66.90184632$ |
1.043305628 |
\( \frac{897469}{3969} a^{2} + \frac{1607729}{3969} a - \frac{153931}{3969} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -a\) , \( a - 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}-a{x}+a-3$ |
| 21.1-a5 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$16.72546158$ |
1.043305628 |
\( \frac{69292788128748168482}{466948881} a^{2} + \frac{83060659682984324659}{466948881} a - \frac{94546406199955131680}{466948881} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -30 a^{2} + 4 a + 10\) , \( -62 a^{2} - 166 a + 150\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-30a^{2}+4a+10\right){x}-62a^{2}-166a+150$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.090682697$ |
1.043305628 |
\( \frac{2905242808362156164576920441}{21609} a^{2} + \frac{3482489114671540668959169161}{21609} a - \frac{3964052911380531038654086531}{21609} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -300 a^{2} - 471 a + 490\) , \( -5356 a^{2} - 7249 a + 7899\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-300a^{2}-471a+490\right){x}-5356a^{2}-7249a+7899$ |
| 21.1-b1 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{16} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.143972128$ |
1.141744332 |
\( -\frac{7508368686128970279577}{299096375126409} a^{2} + \frac{1616589880731750120535}{299096375126409} a + \frac{32458428323711052321331}{299096375126409} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 50 a^{2} + 10 a - 350\) , \( 432 a^{2} + 24 a - 2598\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(50a^{2}+10a-350\right){x}+432a^{2}+24a-2598$ |
| 21.1-b2 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{16} \cdot 7^{2} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$36.60710812$ |
1.141744332 |
\( \frac{95456569237420574}{2109289329} a^{2} - \frac{317812138936041299}{2109289329} a + \frac{237309629218867696}{2109289329} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 10 a^{2} + 15 a - 85\) , \( -27 a^{2} - 50 a + 227\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(10a^{2}+15a-85\right){x}-27a^{2}-50a+227$ |
| 21.1-b3 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$9.151777031$ |
1.141744332 |
\( \frac{69292788128748168482}{466948881} a^{2} + \frac{83060659682984324659}{466948881} a - \frac{94546406199955131680}{466948881} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -10 a^{2} - 15 a - 5\) , \( -65 a^{2} - 88 a + 51\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(-10a^{2}-15a-5\right){x}-65a^{2}-88a+51$ |
| 21.1-b4 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$73.21421624$ |
1.141744332 |
\( \frac{2469125117705}{15752961} a^{2} + \frac{2848919682052}{15752961} a - \frac{3194204179760}{15752961} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -5\) , \( -2 a^{2} - 3 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}-5{x}-2a^{2}-3a+3$ |
| 21.1-b5 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$146.4284324$ |
1.141744332 |
\( \frac{897469}{3969} a^{2} + \frac{1607729}{3969} a - \frac{153931}{3969} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}$ |
| 21.1-b6 |
21.1-b |
$6$ |
$8$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$2.37944$ |
$(a^2-3), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$1.143972128$ |
1.141744332 |
\( \frac{2905242808362156164576920441}{21609} a^{2} + \frac{3482489114671540668959169161}{21609} a - \frac{3964052911380531038654086531}{21609} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -230 a^{2} - 280 a + 340\) , \( -3614 a^{2} - 4360 a + 4812\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(-230a^{2}-280a+340\right){x}-3614a^{2}-4360a+4812$ |
| 24.1-a1 |
24.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{9} \cdot 3^{4} \) |
$2.43299$ |
$(a^2-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$2.555000411$ |
1.434388921 |
\( -\frac{154293134081829766900361}{162} a^{2} + \frac{176796519237114293338739}{648} a + \frac{2594841168555327735277343}{648} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( 981 a^{2} - 259 a - 4177\) , \( 23174 a^{2} - 6568 a - 97609\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(981a^{2}-259a-4177\right){x}+23174a^{2}-6568a-97609$ |
| 24.1-a2 |
24.1-a |
$4$ |
$6$ |
3.3.257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.43299$ |
$(a^2-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$2.555000411$ |
1.434388921 |
\( \frac{9015229605265}{576} a^{2} - \frac{1281213726707}{288} a - \frac{37865221303999}{576} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( 61 a^{2} - 19 a - 257\) , \( 334 a^{2} - 96 a - 1425\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(61a^{2}-19a-257\right){x}+334a^{2}-96a-1425$ |
*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.
