| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$4$ |
$14$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.41455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.339749037 |
\( 16581375 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( 0\) , \( 10 a^{3} - a^{2} - 29 a + 5\) , \( 12 a^{3} + 8 a^{2} - 22 a + 1\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(10a^{3}-a^{2}-29a+5\right){x}+12a^{3}+8a^{2}-22a+1$ |
| 1.1-a2 |
1.1-a |
$4$ |
$14$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.41455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.339749037 |
\( -3375 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( 0\) , \( 5 a^{3} + 4 a^{2} - 4 a + 10\) , \( 13 a^{3} + 10 a^{2} - 20 a + 3\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(5a^{3}+4a^{2}-4a+10\right){x}+13a^{3}+10a^{2}-20a+3$ |
| 1.1-a3 |
1.1-a |
$4$ |
$14$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.41455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.339749037 |
\( 16581375 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -6 a^{3} + 10 a^{2} + 24 a - 31\) , \( 16 a^{3} - 36 a^{2} - 61 a + 95\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-6a^{3}+10a^{2}+24a-31\right){x}+16a^{3}-36a^{2}-61a+95$ |
| 1.1-a4 |
1.1-a |
$4$ |
$14$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$11.41455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
1.339749037 |
\( -3375 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 4 a - 1\) , \( -a^{2} + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-a^{3}+4a-1\right){x}-a^{2}+2$ |
| 7.1-a1 |
7.1-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.392739415$ |
$695.3691245$ |
3.369632941 |
\( \frac{111383156413784305603139}{7} a^{3} - \frac{91636825304740796308315}{7} a^{2} - \frac{553415094848140594418164}{7} a - \frac{94610356275035364328765}{7} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 110 a^{3} - 56 a^{2} - 577 a - 264\) , \( -1122 a^{3} + 699 a^{2} + 5798 a + 2036\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(110a^{3}-56a^{2}-577a-264\right){x}-1122a^{3}+699a^{2}+5798a+2036$ |
| 7.1-a2 |
7.1-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.464246471$ |
$695.3691245$ |
3.369632941 |
\( \frac{363349634}{49} a^{3} - \frac{293867352}{49} a^{2} - \frac{1817432874}{49} a - \frac{310938633}{49} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -a^{2} + 3 a + 6\) , \( a^{3} - a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+3a+6\right){x}+a^{3}-a^{2}-2a+1$ |
| 7.1-a3 |
7.1-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.392739415$ |
$8.584804007$ |
3.369632941 |
\( -\frac{115785963708214013}{7} a^{3} + \frac{433882723088110564}{7} a^{2} - \frac{293930821662511777}{7} a - \frac{66390659360476439}{7} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 10 a^{3} - 46 a^{2} + 48 a + 6\) , \( 67 a^{3} - 296 a^{2} + 314 a - 39\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(10a^{3}-46a^{2}+48a+6\right){x}+67a^{3}-296a^{2}+314a-39$ |
| 7.1-b1 |
7.1-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.289119259$ |
$285.7683425$ |
2.276039842 |
\( -\frac{115785963708214013}{7} a^{3} + \frac{433882723088110564}{7} a^{2} - \frac{293930821662511777}{7} a - \frac{66390659360476439}{7} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - 5 a - 1\) , \( 30 a^{3} - 42 a^{2} - 113 a - 18\) , \( 1419 a^{3} - 1117 a^{2} - 7166 a - 1227\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a^{3}-42a^{2}-113a-18\right){x}+1419a^{3}-1117a^{2}-7166a-1227$ |
| 7.1-b2 |
7.1-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.289119259$ |
$3.528004228$ |
2.276039842 |
\( \frac{111383156413784305603139}{7} a^{3} - \frac{91636825304740796308315}{7} a^{2} - \frac{553415094848140594418164}{7} a - \frac{94610356275035364328765}{7} \) |
\( \bigl[a + 1\) , \( -a^{3} + 5 a + 1\) , \( a^{3} - 4 a - 1\) , \( 15 a^{3} - 57 a^{2} + 30 a\) , \( 100 a^{3} - 309 a^{2} + 74 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(15a^{3}-57a^{2}+30a\right){x}+100a^{3}-309a^{2}+74a+15$ |
| 7.1-b3 |
7.1-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$14.55781$ |
$(-a^3+2a^2+3a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.763039753$ |
$285.7683425$ |
2.276039842 |
\( \frac{363349634}{49} a^{3} - \frac{293867352}{49} a^{2} - \frac{1817432874}{49} a - \frac{310938633}{49} \) |
\( \bigl[a + 1\) , \( -a^{3} + 5 a + 1\) , \( a^{3} - 4 a - 1\) , \( -12 a^{2} + 25 a + 5\) , \( -17 a^{3} + 58 a^{2} - 34 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-12a^{2}+25a+5\right){x}-17a^{3}+58a^{2}-34a-8$ |
| 7.2-a1 |
7.2-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.392739415$ |
$695.3691245$ |
3.369632941 |
\( -\frac{111383156413784305603139}{7} a^{3} + \frac{242512643936612120501102}{7} a^{2} + \frac{402539276216269270225377}{7} a - \frac{628279120014132449452105}{7} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -111 a^{3} + 277 a^{2} + 364 a - 799\) , \( 1288 a^{3} - 3025 a^{2} - 4436 a + 8320\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-111a^{3}+277a^{2}+364a-799\right){x}+1288a^{3}-3025a^{2}-4436a+8320$ |
| 7.2-a2 |
7.2-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{3} \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.464246471$ |
$695.3691245$ |
3.369632941 |
\( -\frac{363349634}{49} a^{3} + \frac{796181550}{49} a^{2} + \frac{1315118676}{49} a - \frac{2058889225}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-a^{3}+2a^{2}+4a-4\right){x}-a^{2}+3$ |
| 7.2-a3 |
7.2-a |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.392739415$ |
$8.584804007$ |
3.369632941 |
\( \frac{115785963708214013}{7} a^{3} + \frac{86524831963468525}{7} a^{2} - \frac{226476733389067312}{7} a - \frac{42224721643091665}{7} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -11 a^{3} - 13 a^{2} + 19 a + 6\) , \( -91 a^{3} - 108 a^{2} + 121 a + 50\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-11a^{3}-13a^{2}+19a+6\right){x}-91a^{3}-108a^{2}+121a+50$ |
| 7.2-b1 |
7.2-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$2.289119259$ |
$3.528004228$ |
2.276039842 |
\( -\frac{111383156413784305603139}{7} a^{3} + \frac{242512643936612120501102}{7} a^{2} + \frac{402539276216269270225377}{7} a - \frac{628279120014132449452105}{7} \) |
\( \bigl[a\) , \( a^{3} - 6 a - 3\) , \( 0\) , \( -22 a^{3} + 64 a - 25\) , \( -110 a^{3} - 67 a^{2} + 242 a - 20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{3}-6a-3\right){x}^{2}+\left(-22a^{3}+64a-25\right){x}-110a^{3}-67a^{2}+242a-20$ |
| 7.2-b2 |
7.2-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{3} \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.763039753$ |
$285.7683425$ |
2.276039842 |
\( -\frac{363349634}{49} a^{3} + \frac{796181550}{49} a^{2} + \frac{1315118676}{49} a - \frac{2058889225}{49} \) |
\( \bigl[a\) , \( a^{3} - 6 a - 3\) , \( 0\) , \( -7 a^{3} + 24 a + 5\) , \( 12 a^{3} + 4 a^{2} - 33 a - 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{3}-6a-3\right){x}^{2}+\left(-7a^{3}+24a+5\right){x}+12a^{3}+4a^{2}-33a-6$ |
| 7.2-b3 |
7.2-b |
$3$ |
$9$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7 \) |
$14.55781$ |
$(a^2-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.289119259$ |
$285.7683425$ |
2.276039842 |
\( \frac{115785963708214013}{7} a^{3} + \frac{86524831963468525}{7} a^{2} - \frac{226476733389067312}{7} a - \frac{42224721643091665}{7} \) |
\( \bigl[1\) , \( a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -31 a^{3} + 50 a^{2} + 110 a - 146\) , \( -1418 a^{3} + 3139 a^{2} + 5136 a - 8086\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+a{x}^{2}+\left(-31a^{3}+50a^{2}+110a-146\right){x}-1418a^{3}+3139a^{2}+5136a-8086$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.14261$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$225.5002019$ |
1.765333563 |
\( -\frac{33018013}{2} a^{3} + 35056779 a^{2} + 63146302 a - 95990009 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -26 a^{3} + 21 a^{2} + 131 a + 25\) , \( -82 a^{3} + 69 a^{2} + 409 a + 68\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-26a^{3}+21a^{2}+131a+25\right){x}-82a^{3}+69a^{2}+409a+68$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.14261$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$308.3870316$ |
2.414215033 |
\( -\frac{33018013}{2} a^{3} + 35056779 a^{2} + 63146302 a - 95990009 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 4 a + 3\) , \( a^{3} - 4 a - 1\) , \( -2 a^{3} - 6 a^{2} + 26 a + 8\) , \( -a^{3} - 21 a^{2} + 53 a + 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(-2a^{3}-6a^{2}+26a+8\right){x}-a^{3}-21a^{2}+53a+11$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.14261$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$308.3870316$ |
2.414215033 |
\( \frac{33018013}{2} a^{3} - \frac{28940481}{2} a^{2} - \frac{167465681}{2} a - \frac{28591869}{2} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a\) , \( -8 a^{3} + 3 a^{2} + 36 a + 14\) , \( -21 a^{3} + a^{2} + 70 a + 7\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-8a^{3}+3a^{2}+36a+14\right){x}-21a^{3}+a^{2}+70a+7$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.14261$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$225.5002019$ |
1.765333563 |
\( \frac{33018013}{2} a^{3} - \frac{28940481}{2} a^{2} - \frac{167465681}{2} a - \frac{28591869}{2} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - 4 a - 2\) , \( 26 a^{3} - 57 a^{2} - 96 a + 144\) , \( 52 a^{3} - 113 a^{2} - 190 a + 289\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(26a^{3}-57a^{2}-96a+144\right){x}+52a^{3}-113a^{2}-190a+289$ |
| 17.1-a1 |
17.1-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$16.26540$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$413.6401340$ |
3.238191387 |
\( -\frac{52354566}{4913} a^{3} + \frac{40253922}{4913} a^{2} + \frac{264541626}{4913} a + \frac{53538489}{4913} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -2 a^{2} + a + 8\) , \( -a^{3} + 3 a\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-2a^{2}+a+8\right){x}-a^{3}+3a$ |
| 17.1-a2 |
17.1-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$16.26540$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$413.6401340$ |
3.238191387 |
\( -\frac{35927415}{17} a^{3} - \frac{26434188}{17} a^{2} + \frac{70640748}{17} a + \frac{12827025}{17} \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{3} - 4 a - 1\) , \( 9 a^{3} - 8 a^{2} - 47 a - 8\) , \( -37 a^{3} + 29 a^{2} + 181 a + 31\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a^{3}-8a^{2}-47a-8\right){x}-37a^{3}+29a^{2}+181a+31$ |
| 17.1-b1 |
17.1-b |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$16.26540$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.129667076$ |
$533.0003637$ |
2.164198337 |
\( -\frac{35927415}{17} a^{3} - \frac{26434188}{17} a^{2} + \frac{70640748}{17} a + \frac{12827025}{17} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 6 a + 5\) , \( -3 a^{3} + 5 a^{2} + 10 a - 15\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(a^{3}-2a^{2}-6a+5\right){x}-3a^{3}+5a^{2}+10a-15$ |
| 17.1-b2 |
17.1-b |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$16.26540$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.043222358$ |
$533.0003637$ |
2.164198337 |
\( -\frac{52354566}{4913} a^{3} + \frac{40253922}{4913} a^{2} + \frac{264541626}{4913} a + \frac{53538489}{4913} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - 2\) , \( 2 a^{3} - 6 a^{2} + 2 a + 3\) , \( 6 a^{3} - 22 a^{2} + 14 a + 4\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(2a^{3}-6a^{2}+2a+3\right){x}+6a^{3}-22a^{2}+14a+4$ |
| 17.2-a1 |
17.2-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{3} \) |
$16.26540$ |
$(a^3-a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$413.6401340$ |
3.238191387 |
\( \frac{52354566}{4913} a^{3} - \frac{116809776}{4913} a^{2} - \frac{187985772}{4913} a + \frac{305979471}{4913} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 3 a^{2} - 5 a + 7\) , \( -2 a^{2} - 2 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(a^{3}-3a^{2}-5a+7\right){x}-2a^{2}-2a+2$ |
| 17.2-a2 |
17.2-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( -17 \) |
$16.26540$ |
$(a^3-a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$413.6401340$ |
3.238191387 |
\( \frac{35927415}{17} a^{3} - \frac{134216433}{17} a^{2} + \frac{90009873}{17} a + \frac{21106170}{17} \) |
\( \bigl[a + 1\) , \( 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -11 a^{3} + 23 a^{2} + 41 a - 57\) , \( 27 a^{3} - 58 a^{2} - 98 a + 149\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+{x}^{2}+\left(-11a^{3}+23a^{2}+41a-57\right){x}+27a^{3}-58a^{2}-98a+149$ |
| 17.2-b1 |
17.2-b |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( -17 \) |
$16.26540$ |
$(a^3-a^2-4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.129667076$ |
$533.0003637$ |
2.164198337 |
\( \frac{35927415}{17} a^{3} - \frac{134216433}{17} a^{2} + \frac{90009873}{17} a + \frac{21106170}{17} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a - 1\) , \( -a - 2\) , \( 2 a^{3} - 3 a^{2} - 13 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-a-2\right){x}+2a^{3}-3a^{2}-13a-3$ |
| 17.2-b2 |
17.2-b |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{3} \) |
$16.26540$ |
$(a^3-a^2-4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.043222358$ |
$533.0003637$ |
2.164198337 |
\( \frac{52354566}{4913} a^{3} - \frac{116809776}{4913} a^{2} - \frac{187985772}{4913} a + \frac{305979471}{4913} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 5\) , \( a + 1\) , \( -a^{3} - 3 a^{2} + 8\) , \( -5 a^{3} - 2 a^{2} + 10 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-5\right){x}^{2}+\left(-a^{3}-3a^{2}+8\right){x}-5a^{3}-2a^{2}+10a-2$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.06873$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.145265415$ |
$3142.127620$ |
3.573270504 |
\( \frac{5712388}{5} a^{3} - \frac{21368707}{5} a^{2} + \frac{14454678}{5} a + \frac{3278693}{5} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{2} - a - 2\) , \( a - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(a-3\right){x}-a^{3}+2a^{2}+4a-6$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.06873$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.290530831$ |
$785.5319051$ |
3.573270504 |
\( -\frac{133975878991962}{5} a^{3} + \frac{2508886729884098}{25} a^{2} - \frac{1699195362540343}{25} a - \frac{383823179004761}{25} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{2} - a - 2\) , \( 10 a^{3} - 20 a^{2} - 34 a + 37\) , \( 16 a^{3} - 37 a^{2} - 60 a + 112\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(10a^{3}-20a^{2}-34a+37\right){x}+16a^{3}-37a^{2}-60a+112$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.06873$ |
$(a^2-a-3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$42.46544505$ |
3.939362636 |
\( -\frac{133975878991962}{5} a^{3} + \frac{2508886729884098}{25} a^{2} - \frac{1699195362540343}{25} a - \frac{383823179004761}{25} \) |
\( \bigl[1\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - 3\) , \( 14 a^{3} - 57 a^{2} + 48 a + 14\) , \( 98 a^{3} - 374 a^{2} + 263 a + 57\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(14a^{3}-57a^{2}+48a+14\right){x}+98a^{3}-374a^{2}+263a+57$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.06873$ |
$(a^2-a-3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$169.8617802$ |
3.939362636 |
\( \frac{5712388}{5} a^{3} - \frac{21368707}{5} a^{2} + \frac{14454678}{5} a + \frac{3278693}{5} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 2\) , \( -a^{2} - a + 3\) , \( 33 a^{3} - 27 a^{2} - 164 a - 29\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-a^{2}-a+3\right){x}+33a^{3}-27a^{2}-164a-29$ |
| 25.1-c1 |
25.1-c |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.06873$ |
$(a^2-a-3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$169.8617802$ |
3.939362636 |
\( -\frac{5712388}{5} a^{3} - \frac{4231543}{5} a^{2} + \frac{11145572}{5} a + \frac{2077052}{5} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 5 a^{3} + 5 a^{2} - 11 a - 7\) , \( -16 a^{3} + 74 a^{2} + 80 a - 172\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(5a^{3}+5a^{2}-11a-7\right){x}-16a^{3}+74a^{2}+80a-172$ |
| 25.1-c2 |
25.1-c |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.06873$ |
$(a^2-a-3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$42.46544505$ |
3.939362636 |
\( \frac{133975878991962}{5} a^{3} + \frac{499248545004668}{25} a^{2} - \frac{1308939912348423}{25} a - \frac{244011206620816}{25} \) |
\( \bigl[1\) , \( a^{3} - 5 a - 3\) , \( a + 1\) , \( -18 a^{3} - 9 a^{2} + 43 a + 8\) , \( -125 a^{3} - 98 a^{2} + 236 a + 44\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-5a-3\right){x}^{2}+\left(-18a^{3}-9a^{2}+43a+8\right){x}-125a^{3}-98a^{2}+236a+44$ |
| 25.1-d1 |
25.1-d |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.06873$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.290530831$ |
$785.5319051$ |
3.573270504 |
\( \frac{133975878991962}{5} a^{3} + \frac{499248545004668}{25} a^{2} - \frac{1308939912348423}{25} a - \frac{244011206620816}{25} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -10 a^{3} + 10 a^{2} + 44 a - 7\) , \( -16 a^{3} + 11 a^{2} + 86 a + 31\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-10a^{3}+10a^{2}+44a-7\right){x}-16a^{3}+11a^{2}+86a+31$ |
| 25.1-d2 |
25.1-d |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.06873$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.145265415$ |
$3142.127620$ |
3.573270504 |
\( -\frac{5712388}{5} a^{3} - \frac{4231543}{5} a^{2} + \frac{11145572}{5} a + \frac{2077052}{5} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -a - 2\) , \( a^{3} - a^{2} - 5 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-a-2\right){x}+a^{3}-a^{2}-5a-1$ |
| 25.3-a1 |
25.3-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.06873$ |
$(a^3-a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.471857436$ |
$269.8335983$ |
3.987003924 |
\( 0 \) |
\( \bigl[0\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( -6 a^{3} - 13 a^{2} + 3 a + 12\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-a^{3}+2a^{2}+6a+1\right){x}-6a^{3}-13a^{2}+3a+12$ |
| 25.3-a2 |
25.3-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.06873$ |
$(a^3-a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.157285812$ |
$269.8335983$ |
3.987003924 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 3\) , \( -a^{2} + a + 5\) , \( 38 a^{3} + 29 a^{2} - 75 a - 18\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+a+5\right){x}+38a^{3}+29a^{2}-75a-18$ |
| 25.4-a1 |
25.4-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.4 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.06873$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.471857436$ |
$269.8335983$ |
3.987003924 |
\( 0 \) |
\( \bigl[0\) , \( -a^{3} + 5 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( 7 a^{3} - 35 a^{2} + 37 a + 7\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-a^{3}+2a^{2}+6a+1\right){x}+7a^{3}-35a^{2}+37a+7$ |
| 25.4-a2 |
25.4-a |
$2$ |
$3$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
25.4 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.06873$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.157285812$ |
$269.8335983$ |
3.987003924 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 3\) , \( -a^{2} + a + 5\) , \( -38 a^{3} + 143 a^{2} - 97 a - 26\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+a+5\right){x}-38a^{3}+143a^{2}-97a-26$ |
| 35.2-a1 |
35.2-a |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7 \) |
$17.80194$ |
$(a+1), (-a^3+2a^2+3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.159473725$ |
$223.1342818$ |
4.457129630 |
\( \frac{1323075862}{4375} a^{3} - \frac{1061976641}{4375} a^{2} - \frac{6527302567}{4375} a - \frac{1115839118}{4375} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} - a - 3\) , \( 3 a^{3} + 3 a^{2} + 2 a + 3\) , \( 6 a^{3} + 11 a^{2} - 5 a - 4\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(3a^{3}+3a^{2}+2a+3\right){x}+6a^{3}+11a^{2}-5a-4$ |
| 35.2-b1 |
35.2-b |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7 \) |
$17.80194$ |
$(a+1), (-a^3+2a^2+3a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.017720437$ |
$1208.252338$ |
5.363668119 |
\( \frac{1323075862}{4375} a^{3} - \frac{1061976641}{4375} a^{2} - \frac{6527302567}{4375} a - \frac{1115839118}{4375} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 3 a^{3} - 7 a^{2} - 11 a + 18\) , \( -12 a^{3} + 26 a^{2} + 43 a - 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(3a^{3}-7a^{2}-11a+18\right){x}-12a^{3}+26a^{2}+43a-68$ |
| 35.3-a1 |
35.3-a |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
35.3 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7 \) |
$17.80194$ |
$(a^3-a^2-5a+1), (a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.159473725$ |
$223.1342818$ |
4.457129630 |
\( -\frac{1323075862}{4375} a^{3} + \frac{581450189}{875} a^{2} + \frac{4682028263}{4375} a - \frac{7382042464}{4375} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a - 1\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( -2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a^{3}-a^{2}-3a+3\right){x}-2$ |
| 35.3-b1 |
35.3-b |
$1$ |
$1$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
35.3 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7 \) |
$17.80194$ |
$(a^3-a^2-5a+1), (a^2-2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.017720437$ |
$1208.252338$ |
5.363668119 |
\( -\frac{1323075862}{4375} a^{3} + \frac{581450189}{875} a^{2} + \frac{4682028263}{4375} a - \frac{7382042464}{4375} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -2 a^{3} + 3 a^{2} + 11 a - 1\) , \( 9 a^{3} - 7 a^{2} - 44 a - 8\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-2a^{3}+3a^{2}+11a-1\right){x}+9a^{3}-7a^{2}-44a-8$ |
| 45.1-a1 |
45.1-a |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{12} \cdot 5 \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$41.38644973$ |
1.943968692 |
\( \frac{1077053360753}{135} a^{3} + \frac{89098485094}{15} a^{2} - \frac{2105021566363}{135} a - \frac{130213771709}{45} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 2\) , \( -3 a^{3} - 2 a^{2} + 3 a + 5\) , \( -6 a^{3} - 27 a^{2} + 42 a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-3a^{3}-2a^{2}+3a+5\right){x}-6a^{3}-27a^{2}+42a-3$ |
| 45.1-a2 |
45.1-a |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$165.5457989$ |
1.943968692 |
\( \frac{1310399}{75} a^{3} + \frac{4858454}{225} a^{2} - \frac{8843402}{225} a - \frac{2351933}{225} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{2} + 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -11 a^{3} + 7 a^{2} + 55 a + 15\) , \( -11 a^{3} + 8 a^{2} + 55 a + 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-11a^{3}+7a^{2}+55a+15\right){x}-11a^{3}+8a^{2}+55a+12$ |
| 45.1-b1 |
45.1-b |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{4} \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.359633246$ |
$826.4059353$ |
4.653321937 |
\( -\frac{10092261043}{1875} a^{3} + \frac{2759394633}{625} a^{2} + \frac{50198968913}{1875} a + \frac{8586304552}{1875} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( 3 a^{3} - 5 a - 3\) , \( 5 a^{3} + 3 a^{2} - 14 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(3a^{3}-5a-3\right){x}+5a^{3}+3a^{2}-14a-3$ |
| 45.1-b2 |
45.1-b |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{8} \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.719266492$ |
$206.6014838$ |
4.653321937 |
\( -\frac{400490286003721}{1171875} a^{3} + \frac{1543858344139103}{1171875} a^{2} - \frac{353262242086338}{390625} a - \frac{238633855609631}{1171875} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} - 35 a^{2} + 10 a + 12\) , \( -32 a^{3} + 143 a^{2} - 114 a - 21\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(13a^{3}-35a^{2}+10a+12\right){x}-32a^{3}+143a^{2}-114a-21$ |
| 45.1-c1 |
45.1-c |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{12} \cdot 5 \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.040372869$ |
$746.6208474$ |
1.415861650 |
\( \frac{1077053360753}{135} a^{3} + \frac{89098485094}{15} a^{2} - \frac{2105021566363}{135} a - \frac{130213771709}{45} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -19 a^{3} + 44 a^{2} + 66 a - 118\) , \( 57 a^{3} - 123 a^{2} - 207 a + 317\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(-19a^{3}+44a^{2}+66a-118\right){x}+57a^{3}-123a^{2}-207a+317$ |
| 45.1-c2 |
45.1-c |
$2$ |
$2$ |
4.4.16317.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$18.37005$ |
$(a+1), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.020186434$ |
$1493.241694$ |
1.415861650 |
\( \frac{1310399}{75} a^{3} + \frac{4858454}{225} a^{2} - \frac{8843402}{225} a - \frac{2351933}{225} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(a^{3}-a^{2}-4a+2\right){x}+a^{3}-a^{2}-4a+2$ |
*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.
