| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 3.1-a1 |
3.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$3.52018$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$181.1877931$ |
1.380901840 |
\( -\frac{65536}{3} a^{2} + 16384 a + \frac{475136}{3} \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( a + 1\) , \( 10 a^{2} - 10 a - 75\) , \( -46 a^{2} + 34 a + 329\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(10a^{2}-10a-75\right){x}-46a^{2}+34a+329$ |
| 3.1-a2 |
3.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$3.52018$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$60.39593105$ |
1.380901840 |
\( \frac{326942720}{27} a^{2} - \frac{253853696}{9} a - \frac{841793536}{27} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 1626159 a^{2} + 5118222 a + 3099975\) , \( 854364241 a^{2} + 2689051843 a + 1628689142\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1626159a^{2}+5118222a+3099975\right){x}+854364241a^{2}+2689051843a+1628689142$ |
| 3.1-a3 |
3.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$3.52018$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$30.19796552$ |
1.380901840 |
\( -\frac{66667103936}{729} a^{2} + \frac{18190790912}{243} a + \frac{488664059824}{729} \) |
\( \bigl[a\) , \( a^{2} - 5\) , \( 1\) , \( -2820457 a^{2} - 8877189 a - 5376677\) , \( 1886921447 a^{2} + 5938953609 a + 3597070571\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-2820457a^{2}-8877189a-5376677\right){x}+1886921447a^{2}+5938953609a+3597070571$ |
| 3.1-a4 |
3.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$3.52018$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$90.59389658$ |
1.380901840 |
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 5\) , \( -2 a^{2} - 8 a - 7\) , \( -13 a^{2} - 44 a - 32\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a^{2}-8a-7\right){x}-13a^{2}-44a-32$ |
| 3.1-b1 |
3.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$3.52018$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.595049933$ |
$91.10340574$ |
1.239490354 |
\( \frac{326942720}{27} a^{2} - \frac{253853696}{9} a - \frac{841793536}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 103466 a^{2} + 325652 a + 197239\) , \( -13846105 a^{2} - 43579649 a - 26395066\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(103466a^{2}+325652a+197239\right){x}-13846105a^{2}-43579649a-26395066$ |
| 3.1-b2 |
3.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$3.52018$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.198349977$ |
$273.3102172$ |
1.239490354 |
\( -\frac{65536}{3} a^{2} + 16384 a + \frac{475136}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 1\) , \( -a - 1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+{x}-a-1$ |
| 3.1-b3 |
3.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$3.52018$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.099174988$ |
$273.3102172$ |
1.239490354 |
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 5\) , \( 346 a^{2} - 808 a - 895\) , \( 930 a^{2} - 2165 a - 2400\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(346a^{2}-808a-895\right){x}+930a^{2}-2165a-2400$ |
| 3.1-b4 |
3.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$3.52018$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.297524966$ |
$91.10340574$ |
1.239490354 |
\( -\frac{66667103936}{729} a^{2} + \frac{18190790912}{243} a + \frac{488664059824}{729} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 5\) , \( -179471 a^{2} - 564779 a - 342053\) , \( -30671436 a^{2} - 96535792 a - 58469149\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-179471a^{2}-564779a-342053\right){x}-30671436a^{2}-96535792a-58469149$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.83346769$ |
1.702113303 |
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( a - 1\) , \( a + 1\) , \( a^{2} - 8 a - 7\) , \( -3 a^{2} - 11 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}-8a-7\right){x}-3a^{2}-11a-7$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.83346769$ |
1.702113303 |
\( \frac{326942720}{27} a^{2} - \frac{253853696}{9} a - \frac{841793536}{27} \) |
\( \bigl[0\) , \( a^{2} - a - 6\) , \( a + 1\) , \( 2054 a^{2} + 6468 a + 3924\) , \( 38872 a^{2} + 122346 a + 74100\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(2054a^{2}+6468a+3924\right){x}+38872a^{2}+122346a+74100$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.83346769$ |
1.702113303 |
\( -\frac{65536}{3} a^{2} + 16384 a + \frac{475136}{3} \) |
\( \bigl[0\) , \( -a^{2} + a + 6\) , \( 1\) , \( 4 a^{2} - 4 a - 30\) , \( 18 a^{2} - 15 a - 133\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(4a^{2}-4a-30\right){x}+18a^{2}-15a-133$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.83346769$ |
1.702113303 |
\( -\frac{66667103936}{729} a^{2} + \frac{18190790912}{243} a + \frac{488664059824}{729} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( -3564 a^{2} - 11220 a - 6792\) , \( 84965 a^{2} + 267417 a + 161965\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-3564a^{2}-11220a-6792\right){x}+84965a^{2}+267417a+161965$ |
| 9.2-b1 |
9.2-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$147.8219580$ |
0.500714658 |
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 17341 a^{2} - 40389 a - 44671\) , \( 224494 a^{2} - 522820 a - 578373\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(17341a^{2}-40389a-44671\right){x}+224494a^{2}-522820a-578373$ |
| 9.2-b2 |
9.2-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$32.84932400$ |
0.500714658 |
\( \frac{326942720}{27} a^{2} - \frac{253853696}{9} a - \frac{841793536}{27} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 130 a^{2} + 414 a + 252\) , \( -755 a^{2} - 2365 a - 1430\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(130a^{2}+414a+252\right){x}-755a^{2}-2365a-1430$ |
| 9.2-b3 |
9.2-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$295.6439160$ |
0.500714658 |
\( -\frac{65536}{3} a^{2} + 16384 a + \frac{475136}{3} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -16 a^{2} + 38 a + 42\) , \( 19 a^{2} - 44 a - 49\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-16a^{2}+38a+42\right){x}+19a^{2}-44a-49$ |
| 9.2-b4 |
9.2-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$4.22751$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$16.42466200$ |
0.500714658 |
\( -\frac{66667103936}{729} a^{2} + \frac{18190790912}{243} a + \frac{488664059824}{729} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 5\) , \( -507 a^{2} - 63 a + 294\) , \( -7094 a^{2} + 8333 a + 11575\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-507a^{2}-63a+294\right){x}-7094a^{2}+8333a+11575$ |
| 12.1-a1 |
12.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{12} \) |
$4.43515$ |
$(a+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$36.56724591$ |
1.672158249 |
\( \frac{1542078968626}{531441} a^{2} + \frac{1618614913934}{177147} a + \frac{2945882857744}{531441} \) |
\( \bigl[a^{2} - a - 4\) , \( a + 1\) , \( a^{2} - a - 4\) , \( -95368771 a^{2} - 300166551 a - 181803117\) , \( -1670786140936 a^{2} - 5258682814024 a - 3185048150802\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-95368771a^{2}-300166551a-181803117\right){x}-1670786140936a^{2}-5258682814024a-3185048150802$ |
| 12.1-a2 |
12.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$4.43515$ |
$(a+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$36.56724591$ |
1.672158249 |
\( \frac{37284740}{729} a^{2} - \frac{29399960}{243} a - \frac{97015312}{729} \) |
\( \bigl[a^{2} - a - 4\) , \( a + 1\) , \( a^{2} - a - 4\) , \( -5780566 a^{2} - 18193926 a - 11019592\) , \( -27764914119 a^{2} - 87388130133 a - 52928729899\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5780566a^{2}-18193926a-11019592\right){x}-27764914119a^{2}-87388130133a-52928729899$ |
| 12.1-a3 |
12.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$4.43515$ |
$(a+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.7017377$ |
1.672158249 |
\( \frac{839532382}{81} a^{2} - \frac{655753486}{27} a - \frac{2124714188}{81} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( 0\) , \( -12 a - 28\) , \( 15 a^{2} - 2 a - 86\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-12a-28\right){x}+15a^{2}-2a-86$ |
| 12.1-a4 |
12.1-a |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$4.43515$ |
$(a+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.7017377$ |
1.672158249 |
\( \frac{12020}{9} a^{2} - \frac{7880}{3} a - \frac{29632}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( 0\) , \( 3 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(3a+7\right){x}$ |
| 12.1-b1 |
12.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{12} \) |
$4.43515$ |
$(a+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.047495006$ |
$73.71272900$ |
2.881695398 |
\( \frac{1542078968626}{531441} a^{2} + \frac{1618614913934}{177147} a + \frac{2945882857744}{531441} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -20508 a^{2} - 64545 a - 39093\) , \( 5222729 a^{2} + 16438176 a + 9956178\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20508a^{2}-64545a-39093\right){x}+5222729a^{2}+16438176a+9956178$ |
| 12.1-b2 |
12.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$4.43515$ |
$(a+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.094990013$ |
$73.71272900$ |
2.881695398 |
\( \frac{37284740}{729} a^{2} - \frac{29399960}{243} a - \frac{97015312}{729} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -1243 a^{2} - 3910 a - 2368\) , \( 84772 a^{2} + 266815 a + 161603\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1243a^{2}-3910a-2368\right){x}+84772a^{2}+266815a+161603$ |
| 12.1-b3 |
12.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$4.43515$ |
$(a+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.284970040$ |
$221.1381870$ |
2.881695398 |
\( \frac{12020}{9} a^{2} - \frac{7880}{3} a - \frac{29632}{9} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -2 a^{2} + 3 a + 5\) , \( 2 a^{2} - 7 a - 8\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+3a+5\right){x}+2a^{2}-7a-8$ |
| 12.1-b4 |
12.1-b |
$4$ |
$6$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$4.43515$ |
$(a+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.142485020$ |
$221.1381870$ |
2.881695398 |
\( \frac{839532382}{81} a^{2} - \frac{655753486}{27} a - \frac{2124714188}{81} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -22 a^{2} + 58 a + 30\) , \( 152 a^{2} - 366 a - 364\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-22a^{2}+58a+30\right){x}+152a^{2}-366a-364$ |
| 13.2-a1 |
13.2-a |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$4.49471$ |
$(-2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.200535939$ |
$203.7245153$ |
3.736376485 |
\( -\frac{46707}{13} a^{2} + \frac{105451}{13} a + \frac{113155}{13} \) |
\( \bigl[1\) , \( a\) , \( a^{2} - 5\) , \( -17 a^{2} - 53 a - 30\) , \( 169 a^{2} + 529 a + 315\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+a{x}^{2}+\left(-17a^{2}-53a-30\right){x}+169a^{2}+529a+315$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$4.49471$ |
$(-2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.156593875$ |
$181.9881681$ |
2.606351855 |
\( -\frac{46707}{13} a^{2} + \frac{105451}{13} a + \frac{113155}{13} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 5\) , \( a\) , \( a^{2} - 2\) , \( a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{2}-2\right){x}+a+1$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$0.199179924$ |
$212.8640489$ |
3.877599946 |
\( -\frac{48625}{2} a^{2} - \frac{165053}{2} a - \frac{229111}{4} \) |
\( \bigl[a^{2} - a - 4\) , \( a + 1\) , \( a^{2} - 4\) , \( -14 a^{2} + 34 a + 34\) , \( 30 a^{2} - 70 a - 80\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a^{2}+34a+34\right){x}+30a^{2}-70a-80$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{15} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$0.398359848$ |
$106.4320244$ |
3.877599946 |
\( \frac{28720234503}{2} a^{2} + 45227442168 a + \frac{54889547245}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a + 1\) , \( a^{2} - 4\) , \( -94 a^{2} + 214 a + 234\) , \( -1038 a^{2} + 2418 a + 2672\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-94a^{2}+214a+234\right){x}-1038a^{2}+2418a+2672$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$4.65298$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$134.7080253$ |
2.053323314 |
\( -290344321040 a^{2} + 237663682586 a + 2128213050144 \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( 0\) , \( 34 a^{2} - 81 a - 82\) , \( 617 a^{2} - 1438 a - 1587\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(34a^{2}-81a-82\right){x}+617a^{2}-1438a-1587$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$4.65298$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$269.4160506$ |
2.053323314 |
\( 221092 a^{2} - 182432 a - 1615488 \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( 0\) , \( -26 a^{2} + 59 a + 73\) , \( 125 a^{2} - 292 a - 319\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-26a^{2}+59a+73\right){x}+125a^{2}-292a-319$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{15} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \) |
$0.173660677$ |
$48.08115601$ |
3.054579990 |
\( \frac{247}{2} a^{2} + \frac{87}{2} a + \frac{695}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 4\) , \( -11 a^{2} + 13 a + 83\) , \( 36 a^{2} - 25 a - 257\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-11a^{2}+13a+83\right){x}+36a^{2}-25a-257$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{15} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \) |
$0.115935683$ |
$63.33109964$ |
2.686020138 |
\( \frac{247}{2} a^{2} + \frac{87}{2} a + \frac{695}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( a\) , \( -2 a + 3\) , \( -a^{2} + a + 4\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-2a+3\right){x}-a^{2}+a+4$ |
| 16.1-e1 |
16.1-e |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$4.65298$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$39.56335790$ |
0.603055126 |
\( -290344321040 a^{2} + 237663682586 a + 2128213050144 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( 22 a^{2} - 25 a - 166\) , \( 75 a^{2} - 60 a - 541\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(22a^{2}-25a-166\right){x}+75a^{2}-60a-541$ |
| 16.1-e2 |
16.1-e |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$4.65298$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$79.12671580$ |
0.603055126 |
\( 221092 a^{2} - 182432 a - 1615488 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( 2 a^{2} - 5 a - 11\) , \( a^{2} - 3 a - 7\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(2a^{2}-5a-11\right){x}+a^{2}-3a-7$ |
| 16.1-f1 |
16.1-f |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{15} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$2.396871639$ |
$9.005618293$ |
1.974119466 |
\( \frac{28720234503}{2} a^{2} + 45227442168 a + \frac{54889547245}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 85 a^{2} - 149 a - 811\) , \( 897 a^{2} - 1423 a - 8181\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(85a^{2}-149a-811\right){x}+897a^{2}-1423a-8181$ |
| 16.1-f2 |
16.1-f |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$4.65298$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1.198435819$ |
$18.01123658$ |
1.974119466 |
\( -\frac{48625}{2} a^{2} - \frac{165053}{2} a - \frac{229111}{4} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 5 a^{2} - 9 a - 51\) , \( 17 a^{2} - 27 a - 157\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(5a^{2}-9a-51\right){x}+17a^{2}-27a-157$ |
| 18.1-a1 |
18.1-a |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$30.12644114$ |
1.836841535 |
\( \frac{3083297}{6} a^{2} - \frac{33126215}{72} a - \frac{92594189}{24} \) |
\( \bigl[a^{2} - 5\) , \( -a\) , \( 1\) , \( 5 a^{2} - 26 a - 86\) , \( 80 a^{2} + 5 a - 422\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(5a^{2}-26a-86\right){x}+80a^{2}+5a-422$ |
| 18.1-b1 |
18.1-b |
$2$ |
$3$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.342178783$ |
$26.54373502$ |
4.984039565 |
\( -\frac{2109094150402}{9} a^{2} - \frac{4425484394159}{6} a - \frac{893467139707}{2} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 6\) , \( a\) , \( -4 a^{2} - 33 a - 52\) , \( 90 a^{2} + 114 a - 224\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-4a^{2}-33a-52\right){x}+90a^{2}+114a-224$ |
| 18.1-b2 |
18.1-b |
$2$ |
$3$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{12} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.114059594$ |
$79.63120507$ |
4.984039565 |
\( -\frac{1087337}{1458} a^{2} - \frac{656297}{243} a - \frac{47005}{81} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( 0\) , \( -156 a^{2} + 127 a + 1146\) , \( -1106 a^{2} + 905 a + 8108\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-156a^{2}+127a+1146\right){x}-1106a^{2}+905a+8108$ |
| 18.1-c1 |
18.1-c |
$2$ |
$5$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{20} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \cdot 3 \) |
$1$ |
$0.533882727$ |
2.441355328 |
\( \frac{204892840941285963152}{59049} a^{2} - \frac{111811123129094053451}{39366} a - \frac{12360962015353146785}{486} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( -17393698 a^{2} + 40511986 a + 44798827\) , \( -312787646561 a^{2} + 728442674758 a + 805851106231\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-17393698a^{2}+40511986a+44798827\right){x}-312787646561a^{2}+728442674758a+805851106231$ |
| 18.1-c2 |
18.1-c |
$2$ |
$5$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$66.73534090$ |
2.441355328 |
\( -\frac{13847}{72} a^{2} - \frac{10199}{32} a - \frac{42359}{32} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 5\) , \( 2 a^{2} - 3 a - 11\) , \( 3 a^{2} - 3 a - 21\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(2a^{2}-3a-11\right){x}+3a^{2}-3a-21$ |
| 18.1-d1 |
18.1-d |
$2$ |
$5$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{20} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.141029690$ |
$11.79346838$ |
4.563399310 |
\( \frac{204892840941285963152}{59049} a^{2} - \frac{111811123129094053451}{39366} a - \frac{12360962015353146785}{486} \) |
\( \bigl[a^{2} - a - 5\) , \( 0\) , \( a^{2} - a - 4\) , \( -3571 a^{2} + 11234 a + 15\) , \( -1841163 a^{2} + 4170017 a + 5114305\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-3571a^{2}+11234a+15\right){x}-1841163a^{2}+4170017a+5114305$ |
| 18.1-d2 |
18.1-d |
$2$ |
$5$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.028205938$ |
$58.96734190$ |
4.563399310 |
\( -\frac{13847}{72} a^{2} - \frac{10199}{32} a - \frac{42359}{32} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -38 a^{2} - 125 a - 84\) , \( -536 a^{2} - 1680 a - 1006\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-38a^{2}-125a-84\right){x}-536a^{2}-1680a-1006$ |
| 18.1-e1 |
18.1-e |
$2$ |
$3$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.217699630$ |
1.320212739 |
\( -\frac{2109094150402}{9} a^{2} - \frac{4425484394159}{6} a - \frac{893467139707}{2} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 4\) , \( -65 a^{2} + 147 a + 167\) , \( -503 a^{2} + 1165 a + 1293\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-65a^{2}+147a+167\right){x}-503a^{2}+1165a+1293$ |
| 18.1-e2 |
18.1-e |
$2$ |
$3$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{12} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$21.65309889$ |
1.320212739 |
\( -\frac{1087337}{1458} a^{2} - \frac{656297}{243} a - \frac{47005}{81} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3347 a^{2} - 7794 a - 8621\) , \( -42990 a^{2} + 100118 a + 110757\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3347a^{2}-7794a-8621\right){x}-42990a^{2}+100118a+110757$ |
| 18.1-f1 |
18.1-f |
$1$ |
$1$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{4} \) |
$4.74522$ |
$(a+2), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.216433896$ |
$36.68662952$ |
1.452373134 |
\( \frac{3083297}{6} a^{2} - \frac{33126215}{72} a - \frac{92594189}{24} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -8 a + 11\) , \( -16 a^{2} + 29 a + 48\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-8a+11\right){x}-16a^{2}+29a+48$ |
| 19.1-a1 |
19.1-a |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$4.78818$ |
$(a^2-2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.63298028$ |
0.354637662 |
\( \frac{2166027242859460}{130321} a^{2} + \frac{6817420001774845}{130321} a + \frac{4129135519267497}{130321} \) |
\( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( a\) , \( -272 a^{2} - 870 a - 547\) , \( -8459 a^{2} - 26640 a - 16164\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-272a^{2}-870a-547\right){x}-8459a^{2}-26640a-16164$ |
| 19.1-a2 |
19.1-a |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$4.78818$ |
$(a^2-2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.26596056$ |
0.354637662 |
\( \frac{39824857}{361} a^{2} - \frac{147432598}{361} a - \frac{147111303}{361} \) |
\( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( a\) , \( -17 a^{2} - 55 a - 32\) , \( -145 a^{2} - 456 a - 277\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17a^{2}-55a-32\right){x}-145a^{2}-456a-277$ |
| 19.1-b1 |
19.1-b |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$4.78818$ |
$(a^2-2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$62.76296393$ |
1.913362724 |
\( \frac{2166027242859460}{130321} a^{2} + \frac{6817420001774845}{130321} a + \frac{4129135519267497}{130321} \) |
\( \bigl[a^{2} - 5\) , \( -1\) , \( 0\) , \( 2 a^{2} + 2 a - 19\) , \( -5 a^{2} + 11 a + 18\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}-{x}^{2}+\left(2a^{2}+2a-19\right){x}-5a^{2}+11a+18$ |
| 19.1-b2 |
19.1-b |
$2$ |
$2$ |
3.3.1076.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$4.78818$ |
$(a^2-2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$125.5259278$ |
1.913362724 |
\( \frac{39824857}{361} a^{2} - \frac{147432598}{361} a - \frac{147111303}{361} \) |
\( \bigl[a^{2} - 5\) , \( -1\) , \( 0\) , \( -3 a^{2} + 7 a + 16\) , \( -4 a^{2} + 8 a + 19\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}-{x}^{2}+\left(-3a^{2}+7a+16\right){x}-4a^{2}+8a+19$ |
*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.
