| 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 |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{18} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$66.32247551$ |
1.694875013 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -12 a^{3} - 19 a^{2} + 73 a + 60\) , \( -50 a^{3} - 59 a^{2} + 276 a + 216\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(-12a^{3}-19a^{2}+73a+60\right){x}-50a^{3}-59a^{2}+276a+216$ |
| 25.1-b1 |
25.1-b |
$4$ |
$14$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$306.1389580$ |
1.955850059 |
\( -3375 \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{2} - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( 12 a^{3} + 17 a^{2} - 69 a - 58\) , \( 16 a^{3} + 20 a^{2} - 89 a - 73\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(12a^{3}+17a^{2}-69a-58\right){x}+16a^{3}+20a^{2}-89a-73$ |
| 25.1-b2 |
25.1-b |
$4$ |
$14$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$306.1389580$ |
1.955850059 |
\( 16581375 \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{2} - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -48 a^{3} - 78 a^{2} + 296 a + 242\) , \( 110 a^{3} + 62 a^{2} - 507 a - 369\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-48a^{3}-78a^{2}+296a+242\right){x}+110a^{3}+62a^{2}-507a-369$ |
| 25.1-b3 |
25.1-b |
$4$ |
$14$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$306.1389580$ |
1.955850059 |
\( -3375 \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( -2 a^{3} - 3 a^{2} + 11 a + 12\) , \( a^{3} + a^{2} - 6 a - 3\) , \( -3 a^{2} - 4 a + 14\) , \( -10 a^{3} - 14 a^{2} + 60 a + 56\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+\left(a^{3}+a^{2}-6a-3\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+11a+12\right){x}^{2}+\left(-3a^{2}-4a+14\right){x}-10a^{3}-14a^{2}+60a+56$ |
| 25.1-b4 |
25.1-b |
$4$ |
$14$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$306.1389580$ |
1.955850059 |
\( 16581375 \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( a^{3} + a^{2} - 6 a - 3\) , \( -3 a^{3} + 3 a^{2} + 56 a - 104\) , \( -50 a^{3} + 120 a^{2} + 242 a - 581\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+\left(a^{3}+a^{2}-6a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+3\right){x}^{2}+\left(-3a^{3}+3a^{2}+56a-104\right){x}-50a^{3}+120a^{2}+242a-581$ |
| 25.1-c1 |
25.1-c |
$4$ |
$35$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/5\Z$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$651.1205096$ |
0.665577015 |
\( -52756480 a^{3} - 52756480 a^{2} + 316538880 a + 125665280 \) |
\( \bigl[0\) , \( 2 a^{3} + 3 a^{2} - 13 a - 11\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -15 a^{3} + 2 a^{2} + 103 a - 56\) , \( 45 a^{3} - 32 a^{2} - 326 a + 353\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-13a-11\right){x}^{2}+\left(-15a^{3}+2a^{2}+103a-56\right){x}+45a^{3}-32a^{2}-326a+353$ |
| 25.1-c2 |
25.1-c |
$4$ |
$35$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$26.04482038$ |
0.665577015 |
\( 52756480 a^{3} + 52756480 a^{2} - 316538880 a - 243630080 \) |
\( \bigl[0\) , \( a^{3} + 2 a^{2} - 6 a - 9\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( 50 a^{3} + 66 a^{2} - 287 a - 225\) , \( 174 a^{3} + 235 a^{2} - 1000 a - 809\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{3}+2a^{2}-6a-9\right){x}^{2}+\left(50a^{3}+66a^{2}-287a-225\right){x}+174a^{3}+235a^{2}-1000a-809$ |
| 25.1-c3 |
25.1-c |
$4$ |
$35$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$26.04482038$ |
0.665577015 |
\( -52756480 a^{3} - 52756480 a^{2} + 316538880 a + 125665280 \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -60 a^{3} - 73 a^{2} + 376 a + 297\) , \( -201 a^{3} - 245 a^{2} + 1267 a + 998\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-60a^{3}-73a^{2}+376a+297\right){x}-201a^{3}-245a^{2}+1267a+998$ |
| 25.1-c4 |
25.1-c |
$4$ |
$35$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\Z/5\Z$ |
$\textsf{potential}$ |
$-35$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$651.1205096$ |
0.665577015 |
\( 52756480 a^{3} + 52756480 a^{2} - 316538880 a - 243630080 \) |
\( \bigl[0\) , \( -a^{3} - 2 a^{2} + 5 a + 9\) , \( a\) , \( 62 a^{3} + 75 a^{2} - 389 a - 299\) , \( -255 a^{3} - 311 a^{2} + 1607 a + 1270\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{3}-2a^{2}+5a+9\right){x}^{2}+\left(62a^{3}+75a^{2}-389a-299\right){x}-255a^{3}-311a^{2}+1607a+1270$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{18} \) |
$10.45765$ |
$(3a^3+4a^2-17a-13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$66.32247551$ |
1.694875013 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 3 a^{3} + 2 a^{2} - 25 a - 19\) , \( 89 a^{3} + 113 a^{2} - 543 a - 431\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(3a^{3}+2a^{2}-25a-19\right){x}+89a^{3}+113a^{2}-543a-431$ |
| 49.1-a1 |
49.1-a |
$2$ |
$5$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{20} \) |
$11.37539$ |
$(-a^3-2a^2+5a+12)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$0.664629997$ |
$237.2301635$ |
3.223419159 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( a^{3} + 2 a^{2} - 6 a - 7\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -2016 a^{3} - 2757 a^{2} + 11621 a + 9369\) , \( 55081 a^{3} + 75161 a^{2} - 318010 a - 256236\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(a^{3}+2a^{2}-6a-7\right){x}^{2}+\left(-2016a^{3}-2757a^{2}+11621a+9369\right){x}+55081a^{3}+75161a^{2}-318010a-256236$ |
| 49.1-a2 |
49.1-a |
$2$ |
$5$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$11.37539$ |
$(-a^3-2a^2+5a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$0.132925999$ |
$237.2301635$ |
3.223419159 |
\( \frac{4096}{7} \) |
\( \bigl[0\) , \( -2 a^{3} - 3 a^{2} + 12 a + 13\) , \( a\) , \( 2 a^{3} - 7 a^{2} - 17 a + 54\) , \( -10 a^{3} + 15 a^{2} + 76 a - 133\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-2a^{3}-3a^{2}+12a+13\right){x}^{2}+\left(2a^{3}-7a^{2}-17a+54\right){x}-10a^{3}+15a^{2}+76a-133$ |
| 49.1-b1 |
49.1-b |
$2$ |
$5$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{20} \) |
$11.37539$ |
$(-a^3-2a^2+5a+12)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$6.653916964$ |
$1.092961923$ |
2.973578042 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 1\) , \( 30 a^{3} + 30 a^{2} - 180 a - 149\) , \( 102 a^{3} + 102 a^{2} - 612 a - 492\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+\left(30a^{3}+30a^{2}-180a-149\right){x}+102a^{3}+102a^{2}-612a-492$ |
| 49.1-b2 |
49.1-b |
$2$ |
$5$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$11.37539$ |
$(-a^3-2a^2+5a+12)$ |
$2$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$0.266156678$ |
$683.1012024$ |
2.973578042 |
\( \frac{4096}{7} \) |
\( \bigl[0\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+{x}$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+a^2-5a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2162663$ |
2.238831327 |
\( -\frac{573485304627}{205379} a^{3} - \frac{806332617709}{205379} a^{2} + \frac{3346741850839}{205379} a + \frac{2708257735800}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a\) , \( 132 a^{3} + 160 a^{2} - 837 a - 663\) , \( 3307 a^{3} + 3992 a^{2} - 20951 a - 16480\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(132a^{3}+160a^{2}-837a-663\right){x}+3307a^{3}+3992a^{2}-20951a-16480$ |
| 59.1-b1 |
59.1-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+a^2-5a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.062194364$ |
$271.9299651$ |
2.593201710 |
\( -\frac{573485304627}{205379} a^{3} - \frac{806332617709}{205379} a^{2} + \frac{3346741850839}{205379} a + \frac{2708257735800}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 6 a - 4\) , \( 21 a^{3} + 29 a^{2} - 121 a - 99\) , \( 26 a^{3} + 36 a^{2} - 150 a - 124\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+\left(a^{3}+a^{2}-6a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(21a^{3}+29a^{2}-121a-99\right){x}+26a^{3}+36a^{2}-150a-124$ |
| 59.1-c1 |
59.1-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+a^2-5a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.065073306$ |
$330.0357331$ |
3.293002336 |
\( \frac{67096438423877205}{205379} a^{3} + \frac{81001640358658630}{205379} a^{2} - \frac{425077720328492143}{205379} a - \frac{334381463093740074}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( 2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{3} + 2 a^{2} - 5 a - 7\) , \( 40 a^{3} + 50 a^{2} - 249 a - 200\) , \( -90 a^{3} - 108 a^{2} + 572 a + 448\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+\left(a^{3}+2a^{2}-5a-7\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-11a-11\right){x}^{2}+\left(40a^{3}+50a^{2}-249a-200\right){x}-90a^{3}-108a^{2}+572a+448$ |
| 59.1-d1 |
59.1-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+a^2-5a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.70901513$ |
0.724601215 |
\( \frac{67096438423877205}{205379} a^{3} + \frac{81001640358658630}{205379} a^{2} - \frac{425077720328492143}{205379} a - \frac{334381463093740074}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 7 a^{3} + 34 a^{2} - 28 a - 189\) , \( -20 a^{3} + 94 a^{2} + 188 a - 672\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+\left(a^{3}+a^{2}-6a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(7a^{3}+34a^{2}-28a-189\right){x}-20a^{3}+94a^{2}+188a-672$ |
| 59.2-a1 |
59.2-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(3a^3+4a^2-18a-17)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2162663$ |
2.238831327 |
\( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{3} - 2 a^{2} + 6 a + 8\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -19 a^{3} + 25 a^{2} + 142 a - 229\) , \( -404 a^{3} + 705 a^{2} + 3109 a - 5954\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+8\right){x}^{2}+\left(-19a^{3}+25a^{2}+142a-229\right){x}-404a^{3}+705a^{2}+3109a-5954$ |
| 59.2-b1 |
59.2-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(3a^3+4a^2-18a-17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.062194364$ |
$271.9299651$ |
2.593201710 |
\( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} + a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 8\) , \( 8 a^{3} + 12 a^{2} - 45 a - 44\) , \( 15 a^{3} + 20 a^{2} - 88 a - 73\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+\left(a^{3}+2a^{2}-5a-8\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(8a^{3}+12a^{2}-45a-44\right){x}+15a^{3}+20a^{2}-88a-73$ |
| 59.2-c1 |
59.2-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(3a^3+4a^2-18a-17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.065073306$ |
$330.0357331$ |
3.293002336 |
\( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 9\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -2 a^{3} + 10 a^{2} + 20 a - 65\) , \( 33 a^{3} - 20 a^{2} - 234 a + 242\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(a^{3}+2a^{2}-5a-9\right){x}^{2}+\left(-2a^{3}+10a^{2}+20a-65\right){x}+33a^{3}-20a^{2}-234a+242$ |
| 59.2-d1 |
59.2-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(3a^3+4a^2-18a-17)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.70901513$ |
0.724601215 |
\( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( a\) , \( 14 a^{3} + 6 a^{2} - 59 a - 52\) , \( 29 a^{3} - 33 a^{2} - 59 a - 22\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+2a^{2}-6a-8\right){x}^{2}+\left(14a^{3}+6a^{2}-59a-52\right){x}+29a^{3}-33a^{2}-59a-22$ |
| 59.3-a1 |
59.3-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2162663$ |
2.238831327 |
\( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 6 a - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -124 a^{3} - 169 a^{2} + 715 a + 576\) , \( -3046 a^{3} - 4155 a^{2} + 17591 a + 14171\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+\left(-124a^{3}-169a^{2}+715a+576\right){x}-3046a^{3}-4155a^{2}+17591a+14171$ |
| 59.3-b1 |
59.3-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.062194364$ |
$271.9299651$ |
2.593201710 |
\( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{2} + a - 5\) , \( a^{3} + a^{2} - 6 a - 4\) , \( 13 a^{3} + 17 a^{2} - 74 a - 56\) , \( 19 a^{3} + 25 a^{2} - 110 a - 87\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+\left(a^{3}+a^{2}-6a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(13a^{3}+17a^{2}-74a-56\right){x}+19a^{3}+25a^{2}-110a-87$ |
| 59.3-c1 |
59.3-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.065073306$ |
$330.0357331$ |
3.293002336 |
\( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \) |
\( \bigl[a\) , \( a^{3} + 2 a^{2} - 7 a - 7\) , \( 2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -34 a^{3} - 44 a^{2} + 193 a + 154\) , \( 83 a^{3} + 115 a^{2} - 481 a - 391\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{3}+3a^{2}-11a-12\right){y}={x}^{3}+\left(a^{3}+2a^{2}-7a-7\right){x}^{2}+\left(-34a^{3}-44a^{2}+193a+154\right){x}+83a^{3}+115a^{2}-481a-391$ |
| 59.3-d1 |
59.3-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.70901513$ |
0.724601215 |
\( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} - a - 3\) , \( a\) , \( 65 a^{3} + 80 a^{2} - 416 a - 328\) , \( 271 a^{3} + 327 a^{2} - 1725 a - 1356\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(65a^{3}+80a^{2}-416a-328\right){x}+271a^{3}+327a^{2}-1725a-1356$ |
| 59.4-a1 |
59.4-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2162663$ |
2.238831327 |
\( \frac{30886657696}{205379} a^{3} + \frac{263733970778}{205379} a^{2} - \frac{91149969253}{205379} a - \frac{1666178595071}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 8\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 2 a^{3} - 27 a^{2} + 32 a + 41\) , \( 141 a^{3} - 545 a^{2} + 263 a + 558\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(2a^{3}-27a^{2}+32a+41\right){x}+141a^{3}-545a^{2}+263a+558$ |
| 59.4-b1 |
59.4-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+2a^2-7a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.062194364$ |
$271.9299651$ |
2.593201710 |
\( \frac{30886657696}{205379} a^{3} + \frac{263733970778}{205379} a^{2} - \frac{91149969253}{205379} a - \frac{1666178595071}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( a^{2} + a - 4\) , \( 1\) , \( 12 a^{3} + 17 a^{2} - 69 a - 58\) , \( 13 a^{3} + 18 a^{2} - 75 a - 62\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(12a^{3}+17a^{2}-69a-58\right){x}+13a^{3}+18a^{2}-75a-62$ |
| 59.4-c1 |
59.4-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+2a^2-7a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.065073306$ |
$330.0357331$ |
3.293002336 |
\( \frac{2881742834304017}{205379} a^{3} - \frac{11023459100477408}{205379} a^{2} + \frac{5208632779404811}{205379} a + \frac{11219844957575165}{205379} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 8\) , \( -a^{2} - a + 3\) , \( a\) , \( -9 a^{2} + 11 a + 26\) , \( -5 a^{3} + 22 a^{2} - 13 a - 29\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-9a^{2}+11a+26\right){x}-5a^{3}+22a^{2}-13a-29$ |
| 59.4-d1 |
59.4-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$11.64255$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.70901513$ |
0.724601215 |
\( \frac{2881742834304017}{205379} a^{3} - \frac{11023459100477408}{205379} a^{2} + \frac{5208632779404811}{205379} a + \frac{11219844957575165}{205379} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( 2 a^{3} + 3 a^{2} - 11 a - 11\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -34 a^{3} - 47 a^{2} + 198 a + 159\) , \( -522 a^{3} - 713 a^{2} + 3016 a + 2430\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-11a-11\right){x}^{2}+\left(-34a^{3}-47a^{2}+198a+159\right){x}-522a^{3}-713a^{2}+3016a+2430$ |
| 71.1-a1 |
71.1-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.880646448$ |
$82.10556773$ |
3.695567517 |
\( \frac{337705309521}{71} a^{3} + \frac{407692977510}{71} a^{2} - \frac{2139474325813}{71} a - \frac{1682987986020}{71} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( 2 a^{3} + 3 a^{2} - 13 a - 12\) , \( 1\) , \( 9 a^{3} + 14 a^{2} - 49 a - 51\) , \( 16 a^{3} + 20 a^{2} - 90 a - 74\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+{y}={x}^{3}+\left(2a^{3}+3a^{2}-13a-12\right){x}^{2}+\left(9a^{3}+14a^{2}-49a-51\right){x}+16a^{3}+20a^{2}-90a-74$ |
| 71.1-b1 |
71.1-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{3} \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.278940957$ |
$74.56956939$ |
3.189349568 |
\( \frac{40567729198}{357911} a^{3} - \frac{18573487223}{357911} a^{2} - \frac{289892232122}{357911} a + \frac{246977548593}{357911} \) |
\( \bigl[1\) , \( 2 a^{3} + 3 a^{2} - 11 a - 12\) , \( a^{3} + 2 a^{2} - 5 a - 8\) , \( 38 a^{3} + 46 a^{2} - 240 a - 187\) , \( 125 a^{3} + 151 a^{2} - 793 a - 627\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+2a^{2}-5a-8\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-11a-12\right){x}^{2}+\left(38a^{3}+46a^{2}-240a-187\right){x}+125a^{3}+151a^{2}-793a-627$ |
| 71.1-c1 |
71.1-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.350817753$ |
$24.25015266$ |
3.348483607 |
\( -\frac{107477168128}{5041} a^{3} - \frac{152866918400}{5041} a^{2} + \frac{629801447424}{5041} a + \frac{510363553792}{5041} \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( 1\) , \( a^{2} + a - 6\) , \( 80 a^{3} - 140 a^{2} - 616 a + 1181\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{2}+a-6\right){x}+80a^{3}-140a^{2}-616a+1181$ |
| 71.1-d1 |
71.1-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.077631787$ |
$821.9823011$ |
3.261437020 |
\( \frac{732083245280}{71} a^{3} - \frac{1278302446217}{71} a^{2} - \frac{5634987718502}{71} a + \frac{10793107895044}{71} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 8\) , \( -2 a^{3} - 3 a^{2} + 11 a + 13\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( a^{3} - 2 a^{2} - 4 a + 8\) , \( 4 a^{3} - 3 a^{2} - 13 a\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+11a+13\right){x}^{2}+\left(a^{3}-2a^{2}-4a+8\right){x}+4a^{3}-3a^{2}-13a$ |
| 71.1-e1 |
71.1-e |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{3} \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.012087042$ |
$1375.479221$ |
2.549190457 |
\( \frac{40567729198}{357911} a^{3} - \frac{18573487223}{357911} a^{2} - \frac{289892232122}{357911} a + \frac{246977548593}{357911} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 7\) , \( -a^{3} - 2 a^{2} + 6 a + 7\) , \( a + 1\) , \( -2 a^{3} - 6 a^{2} + 15 a + 16\) , \( 2 a^{3} - 3 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+7\right){x}^{2}+\left(-2a^{3}-6a^{2}+15a+16\right){x}+2a^{3}-3a^{2}-4a$ |
| 71.1-f1 |
71.1-f |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.316585081$ |
$168.4566808$ |
2.725747549 |
\( \frac{732083245280}{71} a^{3} - \frac{1278302446217}{71} a^{2} - \frac{5634987718502}{71} a + \frac{10793107895044}{71} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -a^{3} - a^{2} + 6 a + 3\) , \( 1\) , \( -a^{3} + 8 a + 2\) , \( 6 a^{3} + 8 a^{2} - 38 a - 36\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+3\right){x}^{2}+\left(-a^{3}+8a+2\right){x}+6a^{3}+8a^{2}-38a-36$ |
| 71.1-g1 |
71.1-g |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.021483562$ |
$2332.543676$ |
2.561197211 |
\( \frac{337705309521}{71} a^{3} + \frac{407692977510}{71} a^{2} - \frac{2139474325813}{71} a - \frac{1682987986020}{71} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{2} + a - 5\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -a^{3} - 3 a^{2} + 6 a + 15\) , \( 44 a^{3} + 61 a^{2} - 254 a - 211\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-12\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-a^{3}-3a^{2}+6a+15\right){x}+44a^{3}+61a^{2}-254a-211$ |
| 71.1-h1 |
71.1-h |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$11.91513$ |
$(-2a^3-2a^2+14a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.021909019$ |
$1115.169704$ |
2.497473303 |
\( -\frac{107477168128}{5041} a^{3} - \frac{152866918400}{5041} a^{2} + \frac{629801447424}{5041} a + \frac{510363553792}{5041} \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -7 a^{3} - 10 a^{2} + 42 a + 34\) , \( 19 a^{3} + 26 a^{2} - 110 a - 89\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a^{3}-10a^{2}+42a+34\right){x}+19a^{3}+26a^{2}-110a-89$ |
| 71.2-a1 |
71.2-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.880646448$ |
$82.10556773$ |
3.695567517 |
\( -\frac{41232704158}{71} a^{3} + \frac{72009764529}{71} a^{2} + \frac{317383892937}{71} a - \frac{607972775628}{71} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{3} + a^{2} - 7 a - 4\) , \( 0\) , \( -3 a^{3} - 6 a^{2} + 19 a + 23\) , \( -7 a^{3} - 11 a^{2} + 41 a + 37\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-7a-4\right){x}^{2}+\left(-3a^{3}-6a^{2}+19a+23\right){x}-7a^{3}-11a^{2}+41a+37$ |
| 71.2-b1 |
71.2-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71^{3} \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.278940957$ |
$74.56956939$ |
3.189349568 |
\( -\frac{6737231751}{357911} a^{3} + \frac{39748625183}{357911} a^{2} - \frac{18717825915}{357911} a - \frac{86019846650}{357911} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a^{3} + 2 a^{2} - 5 a - 8\) , \( -4 a^{3} + 9 a^{2} + 28 a - 66\) , \( -19 a^{3} + 30 a^{2} + 146 a - 267\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+2a^{2}-5a-8\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-4a^{3}+9a^{2}+28a-66\right){x}-19a^{3}+30a^{2}+146a-267$ |
| 71.2-c1 |
71.2-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71^{2} \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.350817753$ |
$24.25015266$ |
3.348483607 |
\( \frac{92210540544}{5041} a^{3} + \frac{107272101888}{5041} a^{2} - \frac{598652993536}{5041} a - \frac{468105109504}{5041} \) |
\( \bigl[0\) , \( -a^{3} - a^{2} + 5 a + 5\) , \( 1\) , \( -3 a^{3} - 4 a^{2} + 17 a + 14\) , \( -30 a^{3} + 105 a^{2} - 40 a - 101\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+5\right){x}^{2}+\left(-3a^{3}-4a^{2}+17a+14\right){x}-30a^{3}+105a^{2}-40a-101$ |
| 71.2-d1 |
71.2-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.077631787$ |
$821.9823011$ |
3.261437020 |
\( -\frac{257492443133}{71} a^{3} + \frac{984995803689}{71} a^{2} - \frac{465431032699}{71} a - \frac{1002554041357}{71} \) |
\( \bigl[a\) , \( a^{2} - a - 5\) , \( a^{3} + 2 a^{2} - 5 a - 7\) , \( -12 a^{3} - 15 a^{2} + 66 a + 56\) , \( -24 a^{3} - 30 a^{2} + 139 a + 107\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+2a^{2}-5a-7\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-12a^{3}-15a^{2}+66a+56\right){x}-24a^{3}-30a^{2}+139a+107$ |
| 71.2-e1 |
71.2-e |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71^{3} \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.012087042$ |
$1375.479221$ |
2.549190457 |
\( -\frac{6737231751}{357911} a^{3} + \frac{39748625183}{357911} a^{2} - \frac{18717825915}{357911} a - \frac{86019846650}{357911} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -15 a^{3} - 20 a^{2} + 86 a + 68\) , \( -25 a^{3} - 34 a^{2} + 145 a + 117\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a^{3}-20a^{2}+86a+68\right){x}-25a^{3}-34a^{2}+145a+117$ |
| 71.2-f1 |
71.2-f |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.316585081$ |
$168.4566808$ |
2.725747549 |
\( -\frac{257492443133}{71} a^{3} + \frac{984995803689}{71} a^{2} - \frac{465431032699}{71} a - \frac{1002554041357}{71} \) |
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( -a^{3} - 2 a^{2} + 6 a + 9\) , \( a\) , \( 3 a^{3} + a^{2} - 18 a + 5\) , \( 7 a^{3} + 8 a^{2} - 42 a - 29\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+9\right){x}^{2}+\left(3a^{3}+a^{2}-18a+5\right){x}+7a^{3}+8a^{2}-42a-29$ |
| 71.2-g1 |
71.2-g |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.021483562$ |
$2332.543676$ |
2.561197211 |
\( -\frac{41232704158}{71} a^{3} + \frac{72009764529}{71} a^{2} + \frac{317383892937}{71} a - \frac{607972775628}{71} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 8\) , \( -2 a^{3} - 3 a^{2} + 11 a + 12\) , \( 0\) , \( 4 a^{3} + 4 a^{2} - 27 a - 14\) , \( -47 a^{3} - 56 a^{2} + 301 a + 239\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){x}{y}={x}^{3}+\left(-2a^{3}-3a^{2}+11a+12\right){x}^{2}+\left(4a^{3}+4a^{2}-27a-14\right){x}-47a^{3}-56a^{2}+301a+239$ |
| 71.2-h1 |
71.2-h |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( 71^{2} \) |
$11.91513$ |
$(7a^3+9a^2-41a-31)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.021909019$ |
$1115.169704$ |
2.497473303 |
\( \frac{92210540544}{5041} a^{3} + \frac{107272101888}{5041} a^{2} - \frac{598652993536}{5041} a - \frac{468105109504}{5041} \) |
\( \bigl[0\) , \( 2 a^{3} + 3 a^{2} - 12 a - 13\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( 4 a^{3} + 4 a^{2} - 27 a - 18\) , \( -21 a^{3} - 25 a^{2} + 134 a + 103\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-12a-13\right){x}^{2}+\left(4a^{3}+4a^{2}-27a-18\right){x}-21a^{3}-25a^{2}+134a+103$ |
| 71.3-a1 |
71.3-a |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(5a^3+7a^2-28a-24)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.880646448$ |
$82.10556773$ |
3.695567517 |
\( \frac{14499836867}{71} a^{3} - \frac{55487831122}{71} a^{2} + \frac{26243447485}{71} a + \frac{56492779821}{71} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - 2 a + 1\) , \( -2 a^{3} - 4 a^{2} + 8 a + 7\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(-a^{2}-2a+1\right){x}-2a^{3}-4a^{2}+8a+7$ |
| 71.3-b1 |
71.3-b |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( 71^{3} \) |
$11.91513$ |
$(5a^3+7a^2-28a-24)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.278940957$ |
$74.56956939$ |
3.189349568 |
\( \frac{171505521527}{357911} a^{3} + \frac{230646737948}{357911} a^{2} - \frac{982547272228}{357911} a - \frac{796389209025}{357911} \) |
\( \bigl[1\) , \( -a^{2} - a + 5\) , \( a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{3} - 8 a^{2} + 5 a + 17\) , \( 3 a^{3} - 24 a^{2} + 24 a + 30\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+2a^{2}-5a-7\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(a^{3}-8a^{2}+5a+17\right){x}+3a^{3}-24a^{2}+24a+30$ |
| 71.3-c1 |
71.3-c |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( 71^{2} \) |
$11.91513$ |
$(5a^3+7a^2-28a-24)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.350817753$ |
$24.25015266$ |
3.348483607 |
\( \frac{13630521344}{5041} a^{3} + \frac{59020271616}{5041} a^{2} - \frac{66721566720}{5041} a - \frac{352246767616}{5041} \) |
\( \bigl[0\) , \( a^{2} - 5\) , \( 1\) , \( a^{3} - 9 a\) , \( 610 a^{3} + 832 a^{2} - 3525 a - 2843\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{3}-9a\right){x}+610a^{3}+832a^{2}-3525a-2843$ |
| 71.3-d1 |
71.3-d |
$1$ |
$1$ |
4.4.6125.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( 71 \) |
$11.91513$ |
$(5a^3+7a^2-28a-24)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.077631787$ |
$821.9823011$ |
3.261437020 |
\( \frac{5520752072949}{71} a^{3} + \frac{7531137764446}{71} a^{2} - \frac{31882024190872}{71} a - \frac{25687141194430}{71} \) |
\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( a^{2} + a - 4\) , \( a^{3} + 2 a^{2} - 6 a - 7\) , \( 10 a^{3} + 12 a^{2} - 62 a - 46\) , \( 35 a^{3} + 41 a^{2} - 221 a - 165\bigr] \) |
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+\left(a^{3}+2a^{2}-6a-7\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(10a^{3}+12a^{2}-62a-46\right){x}+35a^{3}+41a^{2}-221a-165$ |
*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.
