| 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 |
| 3.1-a1 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$234.7941794$ |
1.548995354 |
\( -\frac{231224}{81} a^{2} + \frac{169768}{27} a + \frac{2855377}{81} \) |
\( \bigl[a^{2} - a - 7\) , \( -a\) , \( a^{2} - a - 6\) , \( -52 a^{2} + 127 a + 252\) , \( -204 a^{2} + 505 a + 987\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-52a^{2}+127a+252\right){x}-204a^{2}+505a+987$ |
| 3.1-a2 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$58.69854485$ |
1.548995354 |
\( -\frac{2981345869163015842}{81} a^{2} + \frac{1274847208624236194}{27} a + \frac{27888591297407800427}{81} \) |
\( \bigl[a^{2} - a - 7\) , \( -a\) , \( a^{2} - a - 6\) , \( -522 a^{2} + 1297 a + 2512\) , \( -27178 a^{2} + 67499 a + 131313\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-522a^{2}+1297a+2512\right){x}-27178a^{2}+67499a+131313$ |
| 3.1-a3 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$117.3970897$ |
1.548995354 |
\( -\frac{510170732924}{6561} a^{2} + \frac{217744434820}{2187} a + \frac{4776965753257}{6561} \) |
\( \bigl[a^{2} - a - 7\) , \( -a\) , \( a^{2} - a - 6\) , \( -672 a^{2} + 1667 a + 3247\) , \( -19043 a^{2} + 47294 a + 92010\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-672a^{2}+1667a+3247\right){x}-19043a^{2}+47294a+92010$ |
| 3.1-a4 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$14.67463621$ |
1.548995354 |
\( \frac{7865858604020087938}{43046721} a^{2} - \frac{6511912549951157378}{14348907} a - \frac{38005259809662543851}{43046721} \) |
\( \bigl[a^{2} - a - 7\) , \( -a\) , \( a^{2} - a - 6\) , \( -10742 a^{2} + 26677 a + 51902\) , \( -1185204 a^{2} + 2943585 a + 5726519\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-10742a^{2}+26677a+51902\right){x}-1185204a^{2}+2943585a+5726519$ |
| 3.1-a5 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$58.69854485$ |
1.548995354 |
\( \frac{2612734691}{3} a^{2} - 2164468501 a - \frac{12607407001}{3} \) |
\( \bigl[a^{2} - a - 7\) , \( -a\) , \( a^{2} - a - 6\) , \( -2348111 a^{2} + 5831800 a + 11345282\) , \( 3791563395 a^{2} - 9416770884 a - 18319595785\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-2348111a^{2}+5831800a+11345282\right){x}+3791563395a^{2}-9416770884a-18319595785$ |
| 3.1-a6 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$117.3970897$ |
1.548995354 |
\( \frac{1742}{9} a^{2} - \frac{1432}{3} a - \frac{8209}{9} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 6\) , \( a^{2} - 2 a - 6\) , \( 3 a^{2} - 7 a - 13\) , \( 3 a^{2} - 8 a - 16\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(3a^{2}-7a-13\right){x}+3a^{2}-8a-16$ |
| 3.1-a7 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$14.67463621$ |
1.548995354 |
\( \frac{9294442759126957}{3} a^{2} + 11668973003538517 a + \frac{29612431591541209}{3} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 6\) , \( a^{2} - 2 a - 6\) , \( -1464 a^{2} + 3636 a + 7076\) , \( 1946492 a^{2} - 4834330 a - 9404815\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-1464a^{2}+3636a+7076\right){x}+1946492a^{2}-4834330a-9404815$ |
| 3.1-a8 |
3.1-a |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$117.3970897$ |
1.548995354 |
\( \frac{89266846}{9} a^{2} + \frac{111877444}{3} a + \frac{283688137}{9} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 6\) , \( a^{2} - 2 a - 6\) , \( -8049 a^{2} + 19991 a + 38891\) , \( 732563 a^{2} - 1819402 a - 3539506\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-8049a^{2}+19991a+38891\right){x}+732563a^{2}-1819402a-3539506$ |
| 3.1-b1 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.605138403$ |
$114.9717626$ |
0.688493672 |
\( \frac{1742}{9} a^{2} - \frac{1432}{3} a - \frac{8209}{9} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - a - 8\) , \( a^{2} - a - 6\) , \( 3 a^{2} - 6 a - 18\) , \( a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-a-8\right){x}^{2}+\left(3a^{2}-6a-18\right){x}+a-3$ |
| 3.1-b2 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.210276807$ |
$114.9717626$ |
0.688493672 |
\( \frac{9294442759126957}{3} a^{2} + 11668973003538517 a + \frac{29612431591541209}{3} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - a - 8\) , \( a^{2} - a - 6\) , \( -5480 a^{2} + 13245 a + 27855\) , \( 12927826 a^{2} - 32114315 a - 62438112\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-a-8\right){x}^{2}+\left(-5480a^{2}+13245a+27855\right){x}+12927826a^{2}-32114315a-62438112$ |
| 3.1-b3 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.605138403$ |
$459.8870507$ |
0.688493672 |
\( \frac{89266846}{9} a^{2} + \frac{111877444}{3} a + \frac{283688137}{9} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - a - 8\) , \( a^{2} - a - 6\) , \( -28305 a^{2} + 70440 a + 136230\) , \( 4985274 a^{2} - 12382549 a - 24083205\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-a-8\right){x}^{2}+\left(-28305a^{2}+70440a+136230\right){x}+4985274a^{2}-12382549a-24083205$ |
| 3.1-b4 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.841107231$ |
$3.592867584$ |
0.688493672 |
\( -\frac{2981345869163015842}{81} a^{2} + \frac{1274847208624236194}{27} a + \frac{27888591297407800427}{81} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( 1\) , \( 1042 a^{2} + 882 a - 18098\) , \( -23823 a^{2} + 237901 a - 558082\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(1042a^{2}+882a-18098\right){x}-23823a^{2}+237901a-558082$ |
| 3.1-b5 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.210276807$ |
$229.9435253$ |
0.688493672 |
\( -\frac{231224}{81} a^{2} + \frac{169768}{27} a + \frac{2855377}{81} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( 1\) , \( -168 a^{2} + 432 a + 762\) , \( -563 a^{2} + 1449 a + 2532\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-168a^{2}+432a+762\right){x}-563a^{2}+1449a+2532$ |
| 3.1-b6 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.420553615$ |
$28.74294067$ |
0.688493672 |
\( -\frac{510170732924}{6561} a^{2} + \frac{217744434820}{2187} a + \frac{4776965753257}{6561} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( 1\) , \( -2188 a^{2} + 5652 a + 9757\) , \( -114163 a^{2} + 286425 a + 540722\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-2188a^{2}+5652a+9757\right){x}-114163a^{2}+286425a+540722$ |
| 3.1-b7 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.841107231$ |
$3.592867584$ |
0.688493672 |
\( \frac{7865858604020087938}{43046721} a^{2} - \frac{6511912549951157378}{14348907} a - \frac{38005259809662543851}{43046721} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( 1\) , \( -37738 a^{2} + 93942 a + 181532\) , \( -7702743 a^{2} + 19133573 a + 37206026\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-37738a^{2}+93942a+181532\right){x}-7702743a^{2}+19133573a+37206026$ |
| 3.1-b8 |
3.1-b |
$8$ |
$16$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$4.06664$ |
$(-a^2+3a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.302569201$ |
$459.8870507$ |
0.688493672 |
\( \frac{2612734691}{3} a^{2} - 2164468501 a - \frac{12607407001}{3} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( 1\) , \( -8282587 a^{2} + 20578497 a + 39989504\) , \( 25181156595 a^{2} - 62540800507 a - 121664910154\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-8282587a^{2}+20578497a+39989504\right){x}+25181156595a^{2}-62540800507a-121664910154$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{19} \) |
$4.26638$ |
$(a+2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$8.291631715$ |
3.063309091 |
\( \frac{3450291}{128} a^{2} - 29056 a - \frac{8734269}{32} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 7\) , \( a^{2} - 2 a - 6\) , \( 2 a^{2} - 3 a - 7\) , \( -2 a^{2} - 12 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-3a-7\right){x}^{2}+\left(2a^{2}-3a-7\right){x}-2a^{2}-12a-13$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{19} \) |
$4.26638$ |
$(a+2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.101693341$ |
$52.31082405$ |
0.842283144 |
\( \frac{3450291}{128} a^{2} - 29056 a - \frac{8734269}{32} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 2 a - 7\) , \( a\) , \( 258 a^{2} - 333 a - 2410\) , \( -3799 a^{2} + 4873 a + 35536\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(258a^{2}-333a-2410\right){x}-3799a^{2}+4873a+35536$ |
| 12.1-a1 |
12.1-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$425.2787892$ |
5.611339007 |
\( \frac{984409}{36} a^{2} + \frac{575453}{6} a + \frac{3129097}{36} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 3 a - 6\) , \( a^{2} - a - 6\) , \( -158458 a^{2} + 393547 a + 765614\) , \( 62683370 a^{2} - 155681147 a - 302865568\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-158458a^{2}+393547a+765614\right){x}+62683370a^{2}-155681147a-302865568$ |
| 12.1-a2 |
12.1-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$212.6393946$ |
5.611339007 |
\( \frac{66441904094}{3} a^{2} + \frac{166371917853}{2} a + \frac{421599122557}{6} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 3 a - 6\) , \( a^{2} - a - 6\) , \( -2499293 a^{2} + 6207272 a + 12075764\) , \( 4159360023 a^{2} - 10330234888 a - 20096668846\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-2499293a^{2}+6207272a+12075764\right){x}+4159360023a^{2}-10330234888a-20096668846$ |
| 12.1-a3 |
12.1-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$212.6393946$ |
5.611339007 |
\( -\frac{14080191227}{1296} a^{2} + \frac{1505193475}{108} a + \frac{131711066305}{1296} \) |
\( \bigl[1\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 2096256 a^{2} - 5206285 a - 10128422\) , \( 20165881640 a^{2} - 50084217979 a - 97434952260\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(2096256a^{2}-5206285a-10128422\right){x}+20165881640a^{2}-50084217979a-97434952260$ |
| 12.1-a4 |
12.1-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{5} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$212.6393946$ |
5.611339007 |
\( \frac{7021}{12} a^{2} - 1115 a - \frac{13201}{6} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 6\) , \( a\) , \( -1598 a^{2} + 3968 a + 7722\) , \( -49018 a^{2} + 121741 a + 236838\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-1598a^{2}+3968a+7722\right){x}-49018a^{2}+121741a+236838$ |
| 12.1-b1 |
12.1-b |
$2$ |
$11$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{22} \cdot 3^{11} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.10.1 |
$1$ |
\( 11 \) |
$1$ |
$4.958930795$ |
1.439472964 |
\( -\frac{68915170505}{362797056} a^{2} - \frac{3447025613}{30233088} a + \frac{105325093363}{362797056} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - 2 a - 7\) , \( -4 a^{2} - 2 a + 6\) , \( -13 a^{2} - 16 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+{x}^{2}+\left(-4a^{2}-2a+6\right){x}-13a^{2}-16a-1$ |
| 12.1-b2 |
12.1-b |
$2$ |
$11$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.10.2 |
$121$ |
\( 1 \) |
$1$ |
$0.450811890$ |
1.439472964 |
\( -\frac{2750130292767565637424925553641825}{3} a^{2} + \frac{4553503702084895848087426229384753}{2} a + \frac{26575462314823196373119465391713239}{6} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - 2 a - 7\) , \( -30259 a^{2} + 71173 a + 140916\) , \( -5359984 a^{2} + 13530605 a + 26178851\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+{x}^{2}+\left(-30259a^{2}+71173a+140916\right){x}-5359984a^{2}+13530605a+26178851$ |
| 12.1-c1 |
12.1-c |
$2$ |
$11$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.2 |
$14641$ |
\( 1 \) |
$1$ |
$0.014256189$ |
5.508038618 |
\( -\frac{2750130292767565637424925553641825}{3} a^{2} + \frac{4553503702084895848087426229384753}{2} a + \frac{26575462314823196373119465391713239}{6} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 2 a - 6\) , \( a\) , \( 1289378 a^{2} - 1672697 a - 12107622\) , \( 1394092597 a^{2} - 1790851820 a - 13046998950\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(1289378a^{2}-1672697a-12107622\right){x}+1394092597a^{2}-1790851820a-13046998950$ |
| 12.1-c2 |
12.1-c |
$2$ |
$11$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{22} \cdot 3^{11} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$18.97498806$ |
5.508038618 |
\( -\frac{68915170505}{362797056} a^{2} - \frac{3447025613}{30233088} a + \frac{105325093363}{362797056} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 2 a - 6\) , \( a\) , \( -487 a^{2} + 568 a + 4428\) , \( -35927 a^{2} + 46510 a + 337128\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-487a^{2}+568a+4428\right){x}-35927a^{2}+46510a+337128$ |
| 12.1-d1 |
12.1-d |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{5} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$136.7855586$ |
1.804816418 |
\( \frac{7021}{12} a^{2} - 1115 a - \frac{13201}{6} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 3 a - 8\) , \( a\) , \( 2 a^{2} - 6 a - 12\) , \( a^{2} - 3 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-8\right){x}^{2}+\left(2a^{2}-6a-12\right){x}+a^{2}-3a-6$ |
| 12.1-d2 |
12.1-d |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$34.19638967$ |
1.804816418 |
\( -\frac{14080191227}{1296} a^{2} + \frac{1505193475}{108} a + \frac{131711066305}{1296} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 2 a - 8\) , \( a^{2} - a - 6\) , \( 312 a^{2} - 412 a - 2881\) , \( 5194 a^{2} - 6876 a - 47789\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-2a-8\right){x}^{2}+\left(312a^{2}-412a-2881\right){x}+5194a^{2}-6876a-47789$ |
| 12.1-d3 |
12.1-d |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$68.39277934$ |
1.804816418 |
\( \frac{66441904094}{3} a^{2} + \frac{166371917853}{2} a + \frac{421599122557}{6} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 8\) , \( a\) , \( 11 a^{2} - 3 a - 139\) , \( -72 a^{2} + 73 a + 739\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-8\right){x}^{2}+\left(11a^{2}-3a-139\right){x}-72a^{2}+73a+739$ |
| 12.1-d4 |
12.1-d |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$136.7855586$ |
1.804816418 |
\( \frac{984409}{36} a^{2} + \frac{575453}{6} a + \frac{3129097}{36} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 8\) , \( a\) , \( 6 a^{2} - 8 a - 49\) , \( 6 a^{2} - 9 a - 59\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-8\right){x}^{2}+\left(6a^{2}-8a-49\right){x}+6a^{2}-9a-59$ |
| 12.2-a1 |
12.2-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{4} \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.515643734$ |
$36.57009333$ |
4.478587911 |
\( -\frac{22971101}{81} a^{2} + \frac{9842716}{27} a + \frac{214955695}{81} \) |
\( \bigl[a^{2} - 2 a - 7\) , \( a^{2} - a - 6\) , \( a^{2} - 2 a - 7\) , \( 2 a^{2} - 4 a - 15\) , \( a^{2} - 5 a - 11\bigr] \) |
${y}^2+\left(a^{2}-2a-7\right){x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(2a^{2}-4a-15\right){x}+a^{2}-5a-11$ |
| 12.2-a2 |
12.2-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$1.031287469$ |
$146.2803733$ |
4.478587911 |
\( \frac{2842357}{9} a^{2} - \frac{2342204}{3} a - \frac{13671431}{9} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 6\) , \( a + 1\) , \( -48 a^{2} - 184 a - 156\) , \( 615 a^{2} + 2319 a + 1963\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-48a^{2}-184a-156\right){x}+615a^{2}+2319a+1963$ |
| 12.2-a3 |
12.2-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$2.062574939$ |
$36.57009333$ |
4.478587911 |
\( \frac{2240184385511}{3} a^{2} - 1854582669328 a - \frac{10823838987997}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 6\) , \( a + 1\) , \( 27 a^{2} + 111 a + 99\) , \( 2752 a^{2} + 10369 a + 8773\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(27a^{2}+111a+99\right){x}+2752a^{2}+10369a+8773$ |
| 12.2-a4 |
12.2-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.515643734$ |
$146.2803733$ |
4.478587911 |
\( \frac{37302967}{3} a^{2} + 46832168 a + \frac{118849123}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 6\) , \( a + 1\) , \( -a^{2} + a + 3\) , \( 2 a^{2} - 6 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(-a^{2}+a+3\right){x}+2a^{2}-6a-11$ |
| 12.2-b1 |
12.2-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{4} \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$106.1340274$ |
1.400384931 |
\( -\frac{22971101}{81} a^{2} + \frac{9842716}{27} a + \frac{214955695}{81} \) |
\( \bigl[a^{2} - 2 a - 7\) , \( a^{2} - a - 8\) , \( a^{2} - 2 a - 7\) , \( 624 a^{2} - 800 a - 5837\) , \( -15415 a^{2} + 19775 a + 144197\bigr] \) |
${y}^2+\left(a^{2}-2a-7\right){x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+\left(a^{2}-a-8\right){x}^{2}+\left(624a^{2}-800a-5837\right){x}-15415a^{2}+19775a+144197$ |
| 12.2-b2 |
12.2-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$53.06701372$ |
1.400384931 |
\( \frac{37302967}{3} a^{2} + 46832168 a + \frac{118849123}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - 3 a - 8\) , \( a^{2} - 2 a - 7\) , \( -12 a^{2} + 25 a + 77\) , \( -38 a^{2} + 94 a + 185\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+\left(a^{2}-3a-8\right){x}^{2}+\left(-12a^{2}+25a+77\right){x}-38a^{2}+94a+185$ |
| 12.2-b3 |
12.2-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$106.1340274$ |
1.400384931 |
\( \frac{2842357}{9} a^{2} - \frac{2342204}{3} a - \frac{13671431}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{2} - a - 6\) , \( a^{2} + 3 a\) , \( a^{2} + 5 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{2}+3a\right){x}+a^{2}+5a+3$ |
| 12.2-b4 |
12.2-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$5.12365$ |
$(a+1), (-a^2+3a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$13.26675343$ |
1.400384931 |
\( \frac{2240184385511}{3} a^{2} - 1854582669328 a - \frac{10823838987997}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{2} - a - 6\) , \( -4 a^{2} + 18 a + 15\) , \( -15 a^{2} + 49 a + 66\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a^{2}+18a+15\right){x}-15a^{2}+49a+66$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$5.37530$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.259189332$ |
$224.7088339$ |
3.458139970 |
\( 496 a^{2} + 6176 a + 15744 \) |
\( \bigl[a^{2} - a - 6\) , \( a^{2} - 2 a - 6\) , \( 0\) , \( -16 a^{2} + 42 a + 79\) , \( 19 a^{2} - 46 a - 90\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-16a^{2}+42a+79\right){x}+19a^{2}-46a-90$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$5.37530$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.518378665$ |
$112.3544169$ |
3.458139970 |
\( -1040 a^{2} + 1600 a + 11184 \) |
\( \bigl[0\) , \( a^{2} - 3 a - 6\) , \( 0\) , \( -5 a^{2} - 40 a - 43\) , \( 43 a^{2} + 130 a + 96\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-5a^{2}-40a-43\right){x}+43a^{2}+130a+96$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$5.37530$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3^{2} \) |
$0.057024001$ |
$268.5540353$ |
2.727821333 |
\( 496 a^{2} + 6176 a + 15744 \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 3 a + 6\) , \( 0\) , \( 200 a^{2} - 176 a - 2153\) , \( 4415 a^{2} - 6292 a - 38914\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(200a^{2}-176a-2153\right){x}+4415a^{2}-6292a-38914$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$5.37530$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3^{2} \) |
$0.114048002$ |
$134.2770176$ |
2.727821333 |
\( -1040 a^{2} + 1600 a + 11184 \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 6\) , \( 0\) , \( 4 a^{2} - 10 a - 19\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(4a^{2}-10a-19\right){x}$ |
| 18.3-a1 |
18.3-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{7} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.593606243$ |
$27.36601817$ |
3.215097257 |
\( -\frac{13439627}{96} a^{2} + \frac{1436785}{8} a + \frac{125721001}{96} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 3 a - 7\) , \( 1\) , \( 2 a^{2} - 6 a - 7\) , \( -362 a^{2} + 899 a + 1749\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-7\right){x}^{2}+\left(2a^{2}-6a-7\right){x}-362a^{2}+899a+1749$ |
| 18.3-a2 |
18.3-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.148401560$ |
$54.73203634$ |
3.215097257 |
\( \frac{600351031}{3145728} a^{2} + \frac{18920459}{262144} a + \frac{4226529043}{3145728} \) |
\( \bigl[a^{2} - a - 7\) , \( a - 1\) , \( a + 1\) , \( -271804 a^{2} + 675051 a + 1313288\) , \( 76736709 a^{2} - 190584182 a - 370766709\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-271804a^{2}+675051a+1313288\right){x}+76736709a^{2}-190584182a-370766709$ |
| 18.3-a3 |
18.3-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.296803121$ |
$54.73203634$ |
3.215097257 |
\( \frac{65847613}{9216} a^{2} - \frac{11398439}{768} a - \frac{266269391}{9216} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 8\) , \( a\) , \( -7105 a^{2} + 17645 a + 34332\) , \( -614060 a^{2} + 1525086 a + 2966936\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+8\right){x}^{2}+\left(-7105a^{2}+17645a+34332\right){x}-614060a^{2}+1525086a+2966936$ |
| 18.3-a4 |
18.3-a |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{10} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.593606243$ |
$13.68300908$ |
3.215097257 |
\( \frac{929155770761}{2592} a^{2} - \frac{181618081171}{216} a - \frac{4324585426003}{2592} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 8\) , \( a\) , \( -113145 a^{2} + 281010 a + 546672\) , \( -40022923 a^{2} + 99401395 a + 193377692\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+8\right){x}^{2}+\left(-113145a^{2}+281010a+546672\right){x}-40022923a^{2}+99401395a+193377692$ |
| 18.3-b1 |
18.3-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{8} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.314411513$ |
$91.48705312$ |
5.693012322 |
\( \frac{65847613}{9216} a^{2} - \frac{11398439}{768} a - \frac{266269391}{9216} \) |
\( \bigl[a^{2} - a - 7\) , \( -a - 1\) , \( 1\) , \( -2014 a^{2} + 5000 a + 9737\) , \( -95067 a^{2} + 236109 a + 459335\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2014a^{2}+5000a+9737\right){x}-95067a^{2}+236109a+459335$ |
| 18.3-b2 |
18.3-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{10} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.628823027$ |
$22.87176328$ |
5.693012322 |
\( \frac{929155770761}{2592} a^{2} - \frac{181618081171}{216} a - \frac{4324585426003}{2592} \) |
\( \bigl[a^{2} - a - 7\) , \( -a - 1\) , \( 1\) , \( -32054 a^{2} + 79605 a + 154877\) , \( -6073896 a^{2} + 15085204 a + 29347091\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32054a^{2}+79605a+154877\right){x}-6073896a^{2}+15085204a+29347091$ |
| 18.3-b3 |
18.3-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{7} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.157205756$ |
$91.48705312$ |
5.693012322 |
\( -\frac{13439627}{96} a^{2} + \frac{1436785}{8} a + \frac{125721001}{96} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 2 a^{2} + 6 a + 4\) , \( -33 a^{2} + 219 a + 335\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{2}+6a+4\right){x}-33a^{2}+219a+335$ |
| 18.3-b4 |
18.3-b |
$4$ |
$4$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$5.48186$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.157205756$ |
$45.74352656$ |
5.693012322 |
\( \frac{600351031}{3145728} a^{2} + \frac{18920459}{262144} a + \frac{4226529043}{3145728} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -76995 a^{2} + 191226 a + 372016\) , \( 11614494 a^{2} - 28845892 a - 56117441\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-76995a^{2}+191226a+372016\right){x}+11614494a^{2}-28845892a-56117441$ |
*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.
