| 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 |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1093.349739$ |
0.589264493 |
\( 40800 a^{2} - 10447 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( a^{3} - 5 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -a^{3} - 6 a^{2} - 5 a + 5\) , \( -24 a^{3} - 62 a^{2} + 8 a + 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-a^{3}-6a^{2}-5a+5\right){x}-24a^{3}-62a^{2}+8a+18$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1093.349739$ |
0.589264493 |
\( -49130 a^{2} + 329171 \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( a^{3} - 6 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a+1\right){x}-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-3$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$68.33435874$ |
0.589264493 |
\( -10739384330 a^{2} + 71970652931 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 40 a^{2} - 12\) , \( 10 a^{2} - 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(40a^{2}-12\right){x}+10a^{2}-3$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$68.33435874$ |
0.589264493 |
\( 10739384330 a^{2} - 3205037379 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -40 a^{2} + 268\) , \( -10 a^{2} + 67\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-40a^{2}+268\right){x}-10a^{2}+67$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1093.349739$ |
0.589264493 |
\( 49130 a^{2} - 14739 \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{3} - 6 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 5\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+5\right){x}-1$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.36257$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1093.349739$ |
0.589264493 |
\( -40800 a^{2} + 275153 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( -\frac{73}{2} a^{3} + \frac{41}{2} a^{2} + 241 a - 129\) , \( -261 a^{3} + 144 a^{2} + 1744 a - 955\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+2a+3\right){x}^{2}+\left(-\frac{73}{2}a^{3}+\frac{41}{2}a^{2}+241a-129\right){x}-261a^{3}+144a^{2}+1744a-955$ |
| 5.1-a1 |
5.1-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$494.2042835$ |
2.130824391 |
\( -\frac{3930572}{25} a^{3} - \frac{2203101}{25} a^{2} + \frac{26360696}{25} a + \frac{14676418}{25} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( a^{2} + a - 3\) , \( a + 1\) , \( 2 a^{3} + 4 a^{2} - a + 1\) , \( 3 a^{3} + 8 a^{2} - a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(2a^{3}+4a^{2}-a+1\right){x}+3a^{3}+8a^{2}-a-3$ |
| 5.1-a2 |
5.1-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$494.2042835$ |
2.130824391 |
\( -\frac{654769451}{625} a^{3} + \frac{2137426542}{625} a^{2} + \frac{191546318}{625} a - \frac{636078156}{625} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -a^{3} + 7 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{11}{2} a^{3} + \frac{9}{2} a^{2} + 43 a - 17\) , \( 20 a^{3} - 9 a^{2} - 129 a + 73\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+7a\right){x}^{2}+\left(-\frac{11}{2}a^{3}+\frac{9}{2}a^{2}+43a-17\right){x}+20a^{3}-9a^{2}-129a+73$ |
| 5.1-b1 |
5.1-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.132699177$ |
$2.926034111$ |
1.937236471 |
\( \frac{1344559286738092954873}{1250} a^{3} + \frac{3480711115000927682659}{1250} a^{2} - \frac{200633715664921670157}{625} a - \frac{519388023475360656831}{625} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -422 a^{3} + 67 a^{2} + 2829 a - 445\) , \( \frac{770255}{2} a^{3} + \frac{430809}{2} a^{2} - 2580954 a - 1443543\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-2\right){x}^{2}+\left(-422a^{3}+67a^{2}+2829a-445\right){x}+\frac{770255}{2}a^{3}+\frac{430809}{2}a^{2}-2580954a-1443543$ |
| 5.1-b2 |
5.1-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$4.265398354$ |
$2.926034111$ |
1.937236471 |
\( \frac{233228707970444167769}{50} a^{3} - \frac{127411603245556659623}{50} a^{2} - \frac{781498337194786295021}{25} a + \frac{426928386823029242707}{25} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 203 a^{3} + 138 a^{2} - 1357 a - 919\) , \( 3686 a^{3} + 2144 a^{2} - 24700 a - 14369\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+2\right){x}^{2}+\left(203a^{3}+138a^{2}-1357a-919\right){x}+3686a^{3}+2144a^{2}-24700a-14369$ |
| 5.1-b3 |
5.1-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.421799451$ |
$237.0087630$ |
1.937236471 |
\( \frac{14003393591}{31250} a^{3} - \frac{7947605047}{31250} a^{2} - \frac{46930184419}{15625} a + \frac{26632761123}{15625} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{51}{2} a^{3} + \frac{31}{2} a^{2} - 167 a - 94\) , \( -94 a^{3} - 50 a^{2} + 636 a + 344\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+2\right){x}^{2}+\left(\frac{51}{2}a^{3}+\frac{31}{2}a^{2}-167a-94\right){x}-94a^{3}-50a^{2}+636a+344$ |
| 5.1-b4 |
5.1-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{12} \) |
$12.67181$ |
$(1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.710899725$ |
$237.0087630$ |
1.937236471 |
\( \frac{48644362711833}{488281250} a^{3} + \frac{125505495010589}{488281250} a^{2} - \frac{7850512218797}{244140625} a - \frac{18404481211201}{244140625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( a^{3} - 5 a + 1\) , \( \frac{13}{2} a^{3} - \frac{47}{2} a^{2} + 5 a + 5\) , \( 51 a^{3} - 140 a^{2} - 13 a + 40\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(\frac{13}{2}a^{3}-\frac{47}{2}a^{2}+5a+5\right){x}+51a^{3}-140a^{2}-13a+40$ |
| 5.2-a1 |
5.2-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{4} \) |
$12.67181$ |
$(a^3-7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$494.2042835$ |
2.130824391 |
\( \frac{654769451}{625} a^{3} + \frac{2137426542}{625} a^{2} - \frac{191546318}{625} a - \frac{636078156}{625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( 1\) , \( \frac{13}{2} a^{3} + \frac{9}{2} a^{2} - 41 a - 22\) , \( -\frac{33}{2} a^{3} - \frac{17}{2} a^{2} + 113 a + 62\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}^{2}+\left(\frac{13}{2}a^{3}+\frac{9}{2}a^{2}-41a-22\right){x}-\frac{33}{2}a^{3}-\frac{17}{2}a^{2}+113a+62$ |
| 5.2-a2 |
5.2-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$12.67181$ |
$(a^3-7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$494.2042835$ |
2.130824391 |
\( \frac{3930572}{25} a^{3} - \frac{2203101}{25} a^{2} - \frac{26360696}{25} a + \frac{14676418}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( a^{3} - 5 a + 1\) , \( 1\) , \( 3 a^{3} - 17 a + 7\) , \( \frac{5}{2} a^{3} - \frac{1}{2} a^{2} - 14 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(3a^{3}-17a+7\right){x}+\frac{5}{2}a^{3}-\frac{1}{2}a^{2}-14a+7$ |
| 5.2-b1 |
5.2-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{12} \) |
$12.67181$ |
$(a^3-7a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.710899725$ |
$237.0087630$ |
1.937236471 |
\( -\frac{48644362711833}{488281250} a^{3} + \frac{125505495010589}{488281250} a^{2} + \frac{7850512218797}{244140625} a - \frac{18404481211201}{244140625} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( 1\) , \( a^{3} - 5 a + 1\) , \( -8 a^{3} - 24 a^{2} + 2 a + 7\) , \( -52 a^{3} - 140 a^{2} + 18 a + 40\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+{x}^{2}+\left(-8a^{3}-24a^{2}+2a+7\right){x}-52a^{3}-140a^{2}+18a+40$ |
| 5.2-b2 |
5.2-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$12.67181$ |
$(a^3-7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$4.265398354$ |
$2.926034111$ |
1.937236471 |
\( -\frac{233228707970444167769}{50} a^{3} - \frac{127411603245556659623}{50} a^{2} + \frac{781498337194786295021}{25} a + \frac{426928386823029242707}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( a\) , \( a + 1\) , \( -203 a^{3} + 137 a^{2} + 1362 a - 922\) , \( -\frac{7097}{2} a^{3} + \frac{4165}{2} a^{2} + 23781 a - 13962\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-203a^{3}+137a^{2}+1362a-922\right){x}-\frac{7097}{2}a^{3}+\frac{4165}{2}a^{2}+23781a-13962$ |
| 5.2-b3 |
5.2-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{6} \) |
$12.67181$ |
$(a^3-7a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.421799451$ |
$237.0087630$ |
1.937236471 |
\( -\frac{14003393591}{31250} a^{3} - \frac{7947605047}{31250} a^{2} + \frac{46930184419}{15625} a + \frac{26632761123}{15625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( a\) , \( a + 1\) , \( -\frac{51}{2} a^{3} + \frac{29}{2} a^{2} + 172 a - 97\) , \( 109 a^{3} - 59 a^{2} - 730 a + 396\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{51}{2}a^{3}+\frac{29}{2}a^{2}+172a-97\right){x}+109a^{3}-59a^{2}-730a+396$ |
| 5.2-b4 |
5.2-b |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{4} \) |
$12.67181$ |
$(a^3-7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.132699177$ |
$2.926034111$ |
1.937236471 |
\( -\frac{1344559286738092954873}{1250} a^{3} + \frac{3480711115000927682659}{1250} a^{2} + \frac{200633715664921670157}{625} a - \frac{519388023475360656831}{625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( a^{3} - 6 a + 1\) , \( 423 a^{3} + 65 a^{2} - 2835 a - 439\) , \( -\frac{769067}{2} a^{3} + \frac{430333}{2} a^{2} + 2576975 a - 1441954\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}+\left(a^{3}-6a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}^{2}+\left(423a^{3}+65a^{2}-2835a-439\right){x}-\frac{769067}{2}a^{3}+\frac{430333}{2}a^{2}+2576975a-1441954$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$13.43859$ |
$(-a), (a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.313977272$ |
$944.3642436$ |
2.272774638 |
\( -\frac{1625}{16} a^{2} + \frac{16875}{8} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( 0\) , \( a^{3} - 5 a + 1\) , \( 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( 5 a^{3} + 14 a^{2} + a - 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(2a^{3}+4a^{2}-3a-1\right){x}+5a^{3}+14a^{2}+a-6$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{36} \) |
$13.43859$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.941931816$ |
$11.65881782$ |
2.272774638 |
\( -\frac{12816149125}{4096} a^{2} + \frac{42936379625}{2048} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( 0\) , \( a^{3} - 5 a + 1\) , \( -\frac{31}{2} a^{3} - \frac{97}{2} a^{2} - 8 a + 9\) , \( -239 a^{3} - 634 a^{2} + 53 a + 176\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-\frac{31}{2}a^{3}-\frac{97}{2}a^{2}-8a+9\right){x}-239a^{3}-634a^{2}+53a+176$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{36} \) |
$13.43859$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.883863633$ |
$11.65881782$ |
2.272774638 |
\( \frac{12816149125}{4096} a^{2} - \frac{3840284625}{4096} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( 0\) , \( -\frac{391}{2} a^{3} + \frac{219}{2} a^{2} + 1307 a - 725\) , \( -3296 a^{3} + 1803 a^{2} + 22088 a - 12082\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(-\frac{391}{2}a^{3}+\frac{219}{2}a^{2}+1307a-725\right){x}-3296a^{3}+1803a^{2}+22088a-12082$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$13.43859$ |
$(-a), (a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.627954544$ |
$944.3642436$ |
2.272774638 |
\( \frac{1625}{16} a^{2} + \frac{22375}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( 0\) , \( 17 a^{3} - 8 a^{2} - 118 a + 65\) , \( 26 a^{3} - 13 a^{2} - 178 a + 97\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(17a^{3}-8a^{2}-118a+65\right){x}+26a^{3}-13a^{2}-178a+97$ |
| 8.1-b1 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{16} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{5} \) |
$1$ |
$6.086582547$ |
1.679556602 |
\( \frac{68769820673}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -a^{2} - a + 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -127 a^{3} + 42 a^{2} + 929 a - 499\) , \( -1923 a^{3} + 777 a^{2} + 13748 a - 7447\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-127a^{3}+42a^{2}+929a-499\right){x}-1923a^{3}+777a^{2}+13748a-7447$ |
| 8.1-b2 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$256$ |
\( 2^{3} \) |
$1$ |
$0.380411409$ |
1.679556602 |
\( \frac{5770238117800857605}{2} a^{2} - \frac{3444115276756690051}{4} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{2} + a + 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -63 a^{3} - 488 a^{2} - 869 a - 339\) , \( -5115 a^{3} - 17685 a^{2} - 11724 a - 1979\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-63a^{3}-488a^{2}-869a-339\right){x}-5115a^{3}-17685a^{2}-11724a-1979$ |
| 8.1-b3 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{40} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$97.38532076$ |
1.679556602 |
\( \frac{22041605}{65536} a^{2} - \frac{6591249}{65536} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a^{3} - 6 a\) , \( -\frac{1}{2} a^{3} - \frac{7}{2} a^{2} + 3 a + 5\) , \( -4\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{7}{2}a^{2}+3a+5\right){x}-4$ |
| 8.1-b4 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{40} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$97.38532076$ |
1.679556602 |
\( -\frac{22041605}{65536} a^{2} + \frac{73849993}{32768} \) |
\( \bigl[1\) , \( -a^{2} + 3\) , \( a^{3} - 6 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a^{2} + 3 a - 20\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a^{2}+3a-20\right){x}-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-6$ |
| 8.1-b5 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$256$ |
\( 2^{3} \) |
$1$ |
$0.380411409$ |
1.679556602 |
\( -\frac{5770238117800857605}{2} a^{2} + \frac{77339218372455316419}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -a^{2} - a + 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -2237 a^{3} + 1212 a^{2} + 15069 a - 8339\) , \( -115201 a^{3} + 62759 a^{2} + 772892 a - 422835\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-2237a^{3}+1212a^{2}+15069a-8339\right){x}-115201a^{3}+62759a^{2}+772892a-422835$ |
| 8.1-b6 |
8.1-b |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{32} \) |
$13.43859$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$97.38532076$ |
1.679556602 |
\( \frac{16974593}{256} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{2} + a + 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( 7 a^{3} + 2 a^{2} - 49 a - 19\) , \( 43 a^{3} + 17 a^{2} - 308 a - 167\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(7a^{3}+2a^{2}-49a-19\right){x}+43a^{3}+17a^{2}-308a-167$ |
| 8.2-a1 |
8.2-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.43859$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.314084641$ |
$370.7715859$ |
2.008418857 |
\( 19357 a^{2} - 5298 \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( -2 a^{2} + 5\) , \( -6 a^{2}\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-2a^{2}+5\right){x}-6a^{2}$ |
| 8.2-a2 |
8.2-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.43859$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.157042320$ |
$370.7715859$ |
2.008418857 |
\( -793 a^{2} + 5302 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( -a^{2} + a + 4\) , \( 0\) , \( \frac{3}{2} a^{3} - \frac{3}{2} a^{2} - 10 a + 11\) , \( 2 a^{3} - a^{2} - 14 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{3}{2}a^{2}-10a+11\right){x}+2a^{3}-a^{2}-14a+5$ |
| 10.1-a1 |
10.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{18} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.015092781$ |
$5.860593037$ |
3.666150274 |
\( -\frac{99725941825327813653}{7629394531250} a^{3} - \frac{124449427549520507637}{3814697265625} a^{2} + \frac{29408408141758820927}{3814697265625} a + \frac{90164159167972831857}{7629394531250} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( 5 a^{3} - 18 a^{2} - 13 a + 7\) , \( \frac{89}{2} a^{3} - \frac{321}{2} a^{2} - 13 a + 46\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){x}^{2}+\left(5a^{3}-18a^{2}-13a+7\right){x}+\frac{89}{2}a^{3}-\frac{321}{2}a^{2}-13a+46$ |
| 10.1-a2 |
10.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{9} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$4.030185563$ |
$11.72118607$ |
3.666150274 |
\( \frac{10079293537139435696201}{1953125} a^{3} + \frac{52185291376974023793041}{3906250} a^{2} - \frac{6016086016130706380011}{3906250} a - \frac{7787033896354399355719}{1953125} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{5}{2} a^{3} - \frac{25}{2} a^{2} - 10 a - 5\) , \( -30 a^{3} - 92 a^{2} - 13 a + 8\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{5}{2}a^{3}-\frac{25}{2}a^{2}-10a-5\right){x}-30a^{3}-92a^{2}-13a+8$ |
| 10.1-a3 |
10.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{3} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.343395187$ |
$949.4160720$ |
3.666150274 |
\( \frac{1388349919}{500} a^{3} - \frac{366035249}{250} a^{2} - \frac{9250939217}{500} a + \frac{1261576266}{125} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}$ |
| 10.1-a4 |
10.1-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{6} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.671697593$ |
$474.7080360$ |
3.666150274 |
\( -\frac{15720094}{15625} a^{3} + \frac{6993909}{125000} a^{2} + \frac{206589609}{31250} a - \frac{32903037}{125000} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( a^{3} - 7 a + 1\) , \( 1\) , \( 2 a^{3} - 2 a^{2} - 17 a + 9\) , \( -6 a^{2} - 12 a + 11\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-7a+1\right){x}^{2}+\left(2a^{3}-2a^{2}-17a+9\right){x}-6a^{2}-12a+11$ |
| 10.1-b1 |
10.1-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5 \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.071712851$ |
$1334.275031$ |
2.475339411 |
\( -\frac{2315701288959061}{20} a^{3} - \frac{316263553433727}{5} a^{2} + \frac{15518819439077213}{20} a + \frac{2119462057415261}{5} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{7}{2} a^{3} - \frac{19}{2} a^{2} + 14 a - 31\) , \( -\frac{113}{2} a^{3} + \frac{169}{2} a^{2} + 196 a - 88\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}^{2}+\left(\frac{7}{2}a^{3}-\frac{19}{2}a^{2}+14a-31\right){x}-\frac{113}{2}a^{3}+\frac{169}{2}a^{2}+196a-88$ |
| 10.1-b2 |
10.1-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{4} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.017928212$ |
$667.1375155$ |
2.475339411 |
\( -\frac{4599787}{5000} a^{3} - \frac{14491843}{40000} a^{2} + \frac{29421191}{5000} a + \frac{126405399}{40000} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -a^{3} + 3 a^{2} - 1\) , \( -\frac{5}{2} a^{3} + \frac{11}{2} a^{2} - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-a^{3}+3a^{2}-1\right){x}-\frac{5}{2}a^{3}+\frac{11}{2}a^{2}-2$ |
| 10.1-b3 |
10.1-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.071712851$ |
$1334.275031$ |
2.475339411 |
\( \frac{44124649801}{20} a^{3} - \frac{6026235708}{5} a^{2} - \frac{295704379493}{20} a + \frac{40385400609}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -7 a^{3} + 9 a^{2} + 47 a - 60\) , \( \frac{25}{2} a^{3} - \frac{39}{2} a^{2} - 84 a + 130\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}^{2}+\left(-7a^{3}+9a^{2}+47a-60\right){x}+\frac{25}{2}a^{3}-\frac{39}{2}a^{2}-84a+130$ |
| 10.1-b4 |
10.1-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$13.81871$ |
$(-a), (1/2a^3+1/2a^2-3a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.035856425$ |
$2668.550062$ |
2.475339411 |
\( -\frac{202479023}{50} a^{3} - \frac{445942911}{200} a^{2} + \frac{1357200139}{50} a + \frac{2991762923}{200} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( a^{3} - 7 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{59}{2} a^{3} + \frac{31}{2} a^{2} - 202 a - 95\) , \( -177 a^{3} - 97 a^{2} + 1183 a + 657\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-7a+1\right){x}^{2}+\left(\frac{59}{2}a^{3}+\frac{31}{2}a^{2}-202a-95\right){x}-177a^{3}-97a^{2}+1183a+657$ |
| 10.2-a1 |
10.2-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{9} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 1 \) |
$1$ |
$11.72118607$ |
3.666150274 |
\( -\frac{10079293537139435696201}{1953125} a^{3} + \frac{52185291376974023793041}{3906250} a^{2} + \frac{6016086016130706380011}{3906250} a - \frac{7787033896354399355719}{1953125} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 5 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( a^{3} - 12 a^{2} + 17 a - 7\) , \( \frac{59}{2} a^{3} - \frac{183}{2} a^{2} + 15 a + 6\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(a^{3}-12a^{2}+17a-7\right){x}+\frac{59}{2}a^{3}-\frac{183}{2}a^{2}+15a+6$ |
| 10.2-a2 |
10.2-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{3} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 3 \) |
$1$ |
$949.4160720$ |
3.666150274 |
\( -\frac{1388349919}{500} a^{3} - \frac{366035249}{250} a^{2} + \frac{9250939217}{500} a + \frac{1261576266}{125} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 5 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( -\frac{3}{2} a^{3} + \frac{1}{2} a^{2} + 7 a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+7a-2\right){x}-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-2$ |
| 10.2-a3 |
10.2-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{6} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2^{2} \cdot 3 \) |
$1$ |
$474.7080360$ |
3.666150274 |
\( \frac{15720094}{15625} a^{3} + \frac{6993909}{125000} a^{2} - \frac{206589609}{31250} a - \frac{32903037}{125000} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + 6 a - 5\) , \( a^{3} + 5 a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+6a-5\right){x}+a^{3}+5a^{2}+4a-4$ |
| 10.2-a4 |
10.2-a |
$4$ |
$6$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{18} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2^{2} \) |
$1$ |
$5.860593037$ |
3.666150274 |
\( \frac{99725941825327813653}{7629394531250} a^{3} - \frac{124449427549520507637}{3814697265625} a^{2} - \frac{29408408141758820927}{3814697265625} a + \frac{90164159167972831857}{7629394531250} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( -\frac{11}{2} a^{3} - \frac{35}{2} a^{2} + 16 a + 5\) , \( -45 a^{3} - 160 a^{2} + 16 a + 44\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-1\right){x}^{2}+\left(-\frac{11}{2}a^{3}-\frac{35}{2}a^{2}+16a+5\right){x}-45a^{3}-160a^{2}+16a+44$ |
| 10.2-b1 |
10.2-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{4} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.017928212$ |
$667.1375155$ |
2.475339411 |
\( \frac{4599787}{5000} a^{3} - \frac{14491843}{40000} a^{2} - \frac{29421191}{5000} a + \frac{126405399}{40000} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} + 3 a + 1\) , \( 2 a^{3} + 6 a^{2} + 2 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+3a+1\right){x}+2a^{3}+6a^{2}+2a-4$ |
| 10.2-b2 |
10.2-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5 \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.071712851$ |
$1334.275031$ |
2.475339411 |
\( \frac{2315701288959061}{20} a^{3} - \frac{316263553433727}{5} a^{2} - \frac{15518819439077213}{20} a + \frac{2119462057415261}{5} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{3} + 7 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -457 a^{3} + 248 a^{2} + 3067 a - 1660\) , \( \frac{20581}{2} a^{3} - \frac{11245}{2} a^{2} - 68962 a + 37684\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+7a+1\right){x}^{2}+\left(-457a^{3}+248a^{2}+3067a-1660\right){x}+\frac{20581}{2}a^{3}-\frac{11245}{2}a^{2}-68962a+37684$ |
| 10.2-b3 |
10.2-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.035856425$ |
$2668.550062$ |
2.475339411 |
\( \frac{202479023}{50} a^{3} - \frac{445942911}{200} a^{2} - \frac{1357200139}{50} a + \frac{2991762923}{200} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{3} + 7 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{59}{2} a^{3} + \frac{31}{2} a^{2} + 202 a - 95\) , \( 177 a^{3} - 97 a^{2} - 1183 a + 657\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+7a+1\right){x}^{2}+\left(-\frac{59}{2}a^{3}+\frac{31}{2}a^{2}+202a-95\right){x}+177a^{3}-97a^{2}-1183a+657$ |
| 10.2-b4 |
10.2-b |
$4$ |
$4$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$13.81871$ |
$(-a), (a^3-7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.071712851$ |
$1334.275031$ |
2.475339411 |
\( -\frac{44124649801}{20} a^{3} - \frac{6026235708}{5} a^{2} + \frac{295704379493}{20} a + \frac{40385400609}{5} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -642 a^{3} + 351 a^{2} + 4302 a - 2351\) , \( \frac{37289}{2} a^{3} - \frac{20371}{2} a^{2} - 124947 a + 68258\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}^{2}+\left(-642a^{3}+351a^{2}+4302a-2351\right){x}+\frac{37289}{2}a^{3}-\frac{20371}{2}a^{2}-124947a+68258$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$14.65488$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1805.540084$ |
3.892407430 |
\( -\frac{887825}{2} a^{2} + 2978053 \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{2} + 4\) , \( 0\) , \( -2 a^{2} + 12\) , \( -a^{2} + 7\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+12\right){x}-a^{2}+7$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.65488$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$902.7700420$ |
3.892407430 |
\( -\frac{1037}{4} a^{2} + \frac{5265}{2} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( a\) , \( 2 a^{2} + 4\) , \( -7 a^{2} + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{2}+4\right){x}-7a^{2}+4$ |
| 16.2-a1 |
16.2-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.65488$ |
$(-a)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.155394267$ |
$2155.701715$ |
2.888649253 |
\( 40800 a^{2} - 10447 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{19}{2} a^{3} + \frac{7}{2} a^{2} + 61 a - 32\) , \( -\frac{19}{2} a^{3} + \frac{9}{2} a^{2} + 62 a - 34\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-\frac{19}{2}a^{3}+\frac{7}{2}a^{2}+61a-32\right){x}-\frac{19}{2}a^{3}+\frac{9}{2}a^{2}+62a-34$ |
| 16.2-a2 |
16.2-a |
$6$ |
$8$ |
4.4.13448.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$14.65488$ |
$(-a)$ |
$2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.621577071$ |
$538.9254287$ |
2.888649253 |
\( 10739384330 a^{2} - 3205037379 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( 38 a^{3} - 24 a^{2} - 254 a + 143\) , \( 46 a^{3} - 24 a^{2} - 317 a + 175\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(38a^{3}-24a^{2}-254a+143\right){x}+46a^{3}-24a^{2}-317a+175$ |
*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.
