| 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 |
| 392.1-a1 |
392.1-a |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( \frac{2645848491}{784} a^{5} - \frac{480248907}{392} a^{4} - \frac{1728125484}{49} a^{3} + \frac{1866459527}{98} a^{2} + \frac{3774979591}{49} a - \frac{2321653302}{49} \) |
\( \bigl[\frac{1}{4} a^{4} - a^{2} + a\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a + 1\) , \( -\frac{3}{4} a^{5} - \frac{9}{4} a^{4} + 12 a^{3} + \frac{35}{2} a^{2} - 31 a - 23\) , \( \frac{173}{4} a^{5} + \frac{65}{2} a^{4} - \frac{837}{2} a^{3} - 281 a^{2} + 880 a + 560\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}-a^{2}+a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}\right){x}^{2}+\left(-\frac{3}{4}a^{5}-\frac{9}{4}a^{4}+12a^{3}+\frac{35}{2}a^{2}-31a-23\right){x}+\frac{173}{4}a^{5}+\frac{65}{2}a^{4}-\frac{837}{2}a^{3}-281a^{2}+880a+560$ |
| 392.1-b1 |
392.1-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{1843967547}{21952} a^{5} + \frac{1568932455}{10976} a^{4} - \frac{834514389}{1372} a^{3} - \frac{5860720375}{5488} a^{2} + \frac{1163419821}{5488} a + \frac{280781357}{686} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{5}{2} a^{3} + 2 a^{2} + 7 a - 4\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 3 a - 1\) , \( -\frac{11}{4} a^{5} + \frac{1}{4} a^{4} + \frac{51}{2} a^{3} + 3 a^{2} - 55 a - 17\) , \( -\frac{37}{4} a^{5} - \frac{11}{2} a^{4} + 88 a^{3} + \frac{111}{2} a^{2} - 185 a - 121\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{5}{2}a^{3}+2a^{2}+7a-4\right){x}^{2}+\left(-\frac{11}{4}a^{5}+\frac{1}{4}a^{4}+\frac{51}{2}a^{3}+3a^{2}-55a-17\right){x}-\frac{37}{4}a^{5}-\frac{11}{2}a^{4}+88a^{3}+\frac{111}{2}a^{2}-185a-121$ |
| 392.1-b2 |
392.1-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{29813229161285}{343} a^{5} + \frac{75055229200653}{1372} a^{4} + \frac{1145292315033401}{1372} a^{3} - \frac{360413285025551}{686} a^{2} - \frac{602099786479705}{343} a + \frac{378951908662583}{343} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - a^{2} + a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 1\) , \( \frac{3}{2} a^{5} - \frac{13}{4} a^{4} + 3 a^{3} + \frac{31}{2} a^{2} - 20 a - 15\) , \( \frac{35}{2} a^{5} - \frac{53}{2} a^{4} - 74 a^{3} + 86 a^{2} + 61 a - 8\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-a^{2}+a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}^{2}+\left(\frac{3}{2}a^{5}-\frac{13}{4}a^{4}+3a^{3}+\frac{31}{2}a^{2}-20a-15\right){x}+\frac{35}{2}a^{5}-\frac{53}{2}a^{4}-74a^{3}+86a^{2}+61a-8$ |
| 392.1-c1 |
392.1-c |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( -\frac{5956547}{56} a^{5} + \frac{2292172333}{392} a^{4} - \frac{2228890201}{392} a^{3} - \frac{1241205775}{28} a^{2} + \frac{2029087150}{49} a + \frac{4045133821}{98} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{1}{4} a^{4} + a^{2} + a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( \frac{9}{4} a^{4} + 2 a^{3} - \frac{21}{2} a^{2} - 4 a + 9\) , \( -\frac{5}{4} a^{5} + \frac{27}{4} a^{4} + \frac{49}{2} a^{3} - 35 a^{2} - 63 a + 45\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{4}+a^{2}+a\right){x}^{2}+\left(\frac{9}{4}a^{4}+2a^{3}-\frac{21}{2}a^{2}-4a+9\right){x}-\frac{5}{4}a^{5}+\frac{27}{4}a^{4}+\frac{49}{2}a^{3}-35a^{2}-63a+45$ |
| 392.1-d1 |
392.1-d |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{153380960762007}{2744} a^{5} - \frac{33811899355898}{343} a^{4} - \frac{528398970519755}{1372} a^{3} + \frac{465935160493715}{686} a^{2} + \frac{49312077678597}{343} a - \frac{86983251831132}{343} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 4 a - 2\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 4 a + 1\) , \( 2 a^{5} + 2 a^{4} - \frac{21}{2} a^{3} - 14 a^{2} + 1\) , \( -\frac{31}{4} a^{5} - \frac{27}{4} a^{4} + 51 a^{3} + 64 a^{2} - 23 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+4a-2\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+4a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-3\right){x}^{2}+\left(2a^{5}+2a^{4}-\frac{21}{2}a^{3}-14a^{2}+1\right){x}-\frac{31}{4}a^{5}-\frac{27}{4}a^{4}+51a^{3}+64a^{2}-23a-27$ |
| 392.1-d2 |
392.1-d |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{425250045}{21952} a^{5} - \frac{576961505}{5488} a^{4} - \frac{992554443}{2744} a^{3} + \frac{3046759585}{5488} a^{2} + \frac{5114430243}{5488} a - \frac{1923634157}{2744} \) |
\( \bigl[\frac{1}{4} a^{4} - a^{2} + a - 1\) , \( \frac{1}{4} a^{4} - 2 a^{2} + a + 3\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 1\) , \( \frac{11}{4} a^{5} + \frac{13}{4} a^{4} - \frac{43}{2} a^{3} - 23 a^{2} + 27 a + 22\) , \( \frac{37}{4} a^{5} + \frac{51}{4} a^{4} - 73 a^{3} - \frac{185}{2} a^{2} + 88 a + 73\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}-a^{2}+a-1\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{4}-2a^{2}+a+3\right){x}^{2}+\left(\frac{11}{4}a^{5}+\frac{13}{4}a^{4}-\frac{43}{2}a^{3}-23a^{2}+27a+22\right){x}+\frac{37}{4}a^{5}+\frac{51}{4}a^{4}-73a^{3}-\frac{185}{2}a^{2}+88a+73$ |
| 392.1-e1 |
392.1-e |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{2543722623}{21952} a^{5} - \frac{415009445}{10976} a^{4} + \frac{1642982895}{1372} a^{3} + \frac{1406980395}{2744} a^{2} - \frac{15838330797}{5488} a - \frac{4737594947}{2744} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + 2 a^{3} + \frac{3}{2} a^{2} - 3 a - 2\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a\) , \( \frac{3}{4} a^{5} - \frac{5}{2} a^{4} - 3 a^{3} + \frac{29}{2} a^{2} - 4 a - 9\) , \( 4 a^{5} - \frac{23}{4} a^{4} - \frac{49}{2} a^{3} + \frac{53}{2} a^{2} + 23 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a+2\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+2a^{3}+\frac{3}{2}a^{2}-3a-2\right){x}^{2}+\left(\frac{3}{4}a^{5}-\frac{5}{2}a^{4}-3a^{3}+\frac{29}{2}a^{2}-4a-9\right){x}+4a^{5}-\frac{23}{4}a^{4}-\frac{49}{2}a^{3}+\frac{53}{2}a^{2}+23a-1$ |
| 392.1-e2 |
392.1-e |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{47236851417999}{2744} a^{5} + \frac{60192368222939}{1372} a^{4} - \frac{20700824081997}{343} a^{3} - \frac{52760937734082}{343} a^{2} + \frac{7273604047127}{343} a + \frac{18538623637032}{343} \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{1}{2} a^{3} - 2 a\) , \( \frac{11}{4} a^{5} - \frac{5}{4} a^{4} - 22 a^{3} + \frac{23}{2} a^{2} + 45 a - 24\) , \( -\frac{21}{4} a^{5} + \frac{17}{2} a^{4} + \frac{87}{2} a^{3} - \frac{85}{2} a^{2} - 83 a + 50\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}^{2}+\left(\frac{11}{4}a^{5}-\frac{5}{4}a^{4}-22a^{3}+\frac{23}{2}a^{2}+45a-24\right){x}-\frac{21}{4}a^{5}+\frac{17}{2}a^{4}+\frac{87}{2}a^{3}-\frac{85}{2}a^{2}-83a+50$ |
| 392.1-f1 |
392.1-f |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{2543722623}{21952} a^{5} - \frac{415009445}{10976} a^{4} - \frac{1642982895}{1372} a^{3} + \frac{1406980395}{2744} a^{2} + \frac{15838330797}{5488} a - \frac{4737594947}{2744} \) |
\( \bigl[\frac{1}{4} a^{4} - a^{2} + a\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + 2 a^{3} - a^{2} - 3 a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 3 a - 1\) , \( \frac{47}{4} a^{5} - \frac{27}{4} a^{4} - 112 a^{3} + 71 a^{2} + 238 a - 150\) , \( -\frac{263}{4} a^{5} + \frac{169}{4} a^{4} + \frac{1267}{2} a^{3} - \frac{795}{2} a^{2} - 1330 a + 835\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}-a^{2}+a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+3a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+2a^{3}-a^{2}-3a\right){x}^{2}+\left(\frac{47}{4}a^{5}-\frac{27}{4}a^{4}-112a^{3}+71a^{2}+238a-150\right){x}-\frac{263}{4}a^{5}+\frac{169}{4}a^{4}+\frac{1267}{2}a^{3}-\frac{795}{2}a^{2}-1330a+835$ |
| 392.1-f2 |
392.1-f |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{47236851417999}{2744} a^{5} + \frac{60192368222939}{1372} a^{4} + \frac{20700824081997}{343} a^{3} - \frac{52760937734082}{343} a^{2} - \frac{7273604047127}{343} a + \frac{18538623637032}{343} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + 2 a^{2} + a - 4\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{13}{2} a^{5} + 11 a^{4} - \frac{91}{2} a^{3} - \frac{151}{2} a^{2} + 17 a + 26\) , \( \frac{135}{4} a^{5} + \frac{229}{4} a^{4} - \frac{467}{2} a^{3} - 395 a^{2} + 95 a + 149\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+3a-2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+2a^{2}+a-4\right){x}^{2}+\left(\frac{13}{2}a^{5}+11a^{4}-\frac{91}{2}a^{3}-\frac{151}{2}a^{2}+17a+26\right){x}+\frac{135}{4}a^{5}+\frac{229}{4}a^{4}-\frac{467}{2}a^{3}-395a^{2}+95a+149$ |
| 392.1-g1 |
392.1-g |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( \frac{595761417}{784} a^{5} - \frac{905961713}{196} a^{4} - \frac{3062198743}{392} a^{3} + \frac{4955521371}{196} a^{2} + \frac{145783392}{49} a - \frac{455193775}{49} \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a - 1\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + \frac{5}{2} a^{3} + \frac{3}{2} a^{2} - 5 a - 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - a^{2}\) , \( -9 a^{5} + \frac{25}{4} a^{4} + \frac{173}{2} a^{3} - 58 a^{2} - 183 a + 118\) , \( 91 a^{5} - \frac{227}{4} a^{4} - 873 a^{3} + \frac{1093}{2} a^{2} + 1834 a - 1154\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a-1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-a^{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+\frac{5}{2}a^{3}+\frac{3}{2}a^{2}-5a-2\right){x}^{2}+\left(-9a^{5}+\frac{25}{4}a^{4}+\frac{173}{2}a^{3}-58a^{2}-183a+118\right){x}+91a^{5}-\frac{227}{4}a^{4}-873a^{3}+\frac{1093}{2}a^{2}+1834a-1154$ |
| 392.1-h1 |
392.1-h |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{1843967547}{21952} a^{5} + \frac{1568932455}{10976} a^{4} + \frac{834514389}{1372} a^{3} - \frac{5860720375}{5488} a^{2} - \frac{1163419821}{5488} a + \frac{280781357}{686} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + 2 a^{2} - a - 4\) , \( \frac{1}{4} a^{4} - a^{2} + a - 1\) , \( \frac{9}{4} a^{5} - \frac{9}{4} a^{4} - 20 a^{3} + 20 a^{2} + 38 a - 28\) , \( \frac{29}{4} a^{5} - \frac{11}{4} a^{4} - \frac{133}{2} a^{3} + \frac{67}{2} a^{2} + 135 a - 79\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{4}a^{4}-a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+2a^{2}-a-4\right){x}^{2}+\left(\frac{9}{4}a^{5}-\frac{9}{4}a^{4}-20a^{3}+20a^{2}+38a-28\right){x}+\frac{29}{4}a^{5}-\frac{11}{4}a^{4}-\frac{133}{2}a^{3}+\frac{67}{2}a^{2}+135a-79$ |
| 392.1-h2 |
392.1-h |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( \frac{29813229161285}{343} a^{5} + \frac{75055229200653}{1372} a^{4} - \frac{1145292315033401}{1372} a^{3} - \frac{360413285025551}{686} a^{2} + \frac{602099786479705}{343} a + \frac{378951908662583}{343} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 1\) , \( -\frac{1}{4} a^{4} + \frac{3}{2} a^{2} - 2\) , \( 1\) , \( \frac{13}{4} a^{5} - \frac{1}{2} a^{4} - \frac{59}{2} a^{3} + 7 a^{2} + 52 a - 28\) , \( -\frac{19}{2} a^{5} + 4 a^{4} + 88 a^{3} - 43 a^{2} - 173 a + 104\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{4}+\frac{3}{2}a^{2}-2\right){x}^{2}+\left(\frac{13}{4}a^{5}-\frac{1}{2}a^{4}-\frac{59}{2}a^{3}+7a^{2}+52a-28\right){x}-\frac{19}{2}a^{5}+4a^{4}+88a^{3}-43a^{2}-173a+104$ |
| 392.1-i1 |
392.1-i |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( -\frac{2645848491}{784} a^{5} - \frac{480248907}{392} a^{4} + \frac{1728125484}{49} a^{3} + \frac{1866459527}{98} a^{2} - \frac{3774979591}{49} a - \frac{2321653302}{49} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 1\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + 2 a^{3} - \frac{3}{2} a^{2} - 2 a + 1\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 1\) , \( \frac{19}{4} a^{5} - 3 a^{4} - 42 a^{3} + \frac{59}{2} a^{2} + 78 a - 50\) , \( -\frac{637}{4} a^{5} + 101 a^{4} + 1535 a^{3} - 967 a^{2} - 3244 a + 2042\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+2a^{3}-\frac{3}{2}a^{2}-2a+1\right){x}^{2}+\left(\frac{19}{4}a^{5}-3a^{4}-42a^{3}+\frac{59}{2}a^{2}+78a-50\right){x}-\frac{637}{4}a^{5}+101a^{4}+1535a^{3}-967a^{2}-3244a+2042$ |
| 392.1-j1 |
392.1-j |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( -\frac{595761417}{784} a^{5} - \frac{905961713}{196} a^{4} + \frac{3062198743}{392} a^{3} + \frac{4955521371}{196} a^{2} - \frac{145783392}{49} a - \frac{455193775}{49} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{3}{2} a^{3} - 2 a^{2} - a + 2\) , \( \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{5} - \frac{1}{4} a^{4} - \frac{5}{2} a^{3} - \frac{3}{2} a^{2} + a + 8\) , \( -a^{5} + \frac{1}{4} a^{4} + \frac{15}{2} a^{3} + \frac{3}{2} a^{2} - 13 a - 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+a-2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{3}{2}a^{3}-2a^{2}-a+2\right){x}^{2}+\left(\frac{1}{2}a^{5}-\frac{1}{4}a^{4}-\frac{5}{2}a^{3}-\frac{3}{2}a^{2}+a+8\right){x}-a^{5}+\frac{1}{4}a^{4}+\frac{15}{2}a^{3}+\frac{3}{2}a^{2}-13a-7$ |
| 392.1-k1 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{108} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$6561$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.082990635$ |
2.20992 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 392.1-k2 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$44104.62610$ |
2.20992 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 392.1-k3 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{18} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$9$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$60.50017298$ |
2.20992 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 392.1-k4 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{36} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3Cs.1.1 |
$9$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$60.50017298$ |
2.20992 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 392.1-k5 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$44104.62610$ |
2.20992 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 392.1-k6 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{45} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.562521623$ |
2.20992 |
\( -\frac{392127492092318125}{221460595216} a^{5} + \frac{392127492092318125}{27682574402} a^{3} - \frac{1176382476276954375}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{65}{2} a^{5} - 260 a^{3} + 390 a - 356\) , \( 500 a^{5} - 4000 a^{3} + 6000 a - 2038\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{65}{2}a^{5}-260a^{3}+390a-356\right){x}+500a^{5}-4000a^{3}+6000a-2038$ |
| 392.1-k7 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{45} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$7.562521623$ |
2.20992 |
\( \frac{392127492092318125}{221460595216} a^{5} - \frac{392127492092318125}{27682574402} a^{3} + \frac{1176382476276954375}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{65}{2} a^{5} + 260 a^{3} - 390 a - 356\) , \( -500 a^{5} + 4000 a^{3} - 6000 a - 2038\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{65}{2}a^{5}+260a^{3}-390a-356\right){x}-500a^{5}+4000a^{3}-6000a-2038$ |
| 392.1-k8 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{54} \cdot 7^{12} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$6561$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.082990635$ |
2.20992 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 392.1-k9 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$5513.078263$ |
2.20992 |
\( -\frac{2928743223192875}{19208} a^{5} + \frac{2928743223192875}{2401} a^{3} - \frac{8786229669578625}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{55}{4} a^{5} - 110 a^{3} + 165 a - 91\) , \( -\frac{145}{2} a^{5} + 580 a^{3} - 870 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{55}{4}a^{5}-110a^{3}+165a-91\right){x}-\frac{145}{2}a^{5}+580a^{3}-870a+416$ |
| 392.1-k10 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$5513.078263$ |
2.20992 |
\( \frac{2928743223192875}{19208} a^{5} - \frac{2928743223192875}{2401} a^{3} + \frac{8786229669578625}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{55}{4} a^{5} + 110 a^{3} - 165 a - 91\) , \( \frac{145}{2} a^{5} - 580 a^{3} + 870 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{55}{4}a^{5}+110a^{3}-165a-91\right){x}+\frac{145}{2}a^{5}-580a^{3}+870a+416$ |
| 392.1-k11 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{27} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$26244$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.010373829$ |
2.20992 |
\( -\frac{218768831290078842857759125}{307328} a^{5} + \frac{218768831290078842857759125}{38416} a^{3} - \frac{656306493870236528573277375}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 3620 a^{5} - 28960 a^{3} + 43440 a - 23211\) , \( 306120 a^{5} - 2448960 a^{3} + 3673440 a - 1786730\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(3620a^{5}-28960a^{3}+43440a-23211\right){x}+306120a^{5}-2448960a^{3}+3673440a-1786730$ |
| 392.1-k12 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{27} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$26244$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.010373829$ |
2.20992 |
\( \frac{218768831290078842857759125}{307328} a^{5} - \frac{218768831290078842857759125}{38416} a^{3} + \frac{656306493870236528573277375}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3620 a^{5} + 28960 a^{3} - 43440 a - 23211\) , \( -306120 a^{5} + 2448960 a^{3} - 3673440 a - 1786730\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-3620a^{5}+28960a^{3}-43440a-23211\right){x}-306120a^{5}+2448960a^{3}-3673440a-1786730$ |
| 392.1-l1 |
392.1-l |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{153380960762007}{2744} a^{5} - \frac{33811899355898}{343} a^{4} + \frac{528398970519755}{1372} a^{3} + \frac{465935160493715}{686} a^{2} - \frac{49312077678597}{343} a - \frac{86983251831132}{343} \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{2} + a + 3\) , \( 0\) , \( \frac{37}{4} a^{5} - \frac{23}{4} a^{4} - 92 a^{3} + \frac{113}{2} a^{2} + 207 a - 123\) , \( \frac{283}{4} a^{5} - 46 a^{4} - 677 a^{3} + 434 a^{2} + 1413 a - 879\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+3\right){x}^{2}+\left(\frac{37}{4}a^{5}-\frac{23}{4}a^{4}-92a^{3}+\frac{113}{2}a^{2}+207a-123\right){x}+\frac{283}{4}a^{5}-46a^{4}-677a^{3}+434a^{2}+1413a-879$ |
| 392.1-l2 |
392.1-l |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{21} \cdot 7^{8} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$908.4027061$ |
0.819308 |
\( -\frac{425250045}{21952} a^{5} - \frac{576961505}{5488} a^{4} + \frac{992554443}{2744} a^{3} + \frac{3046759585}{5488} a^{2} - \frac{5114430243}{5488} a - \frac{1923634157}{2744} \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 2 a + 1\) , \( -\frac{1}{4} a^{5} + \frac{5}{2} a^{3} - 7 a - 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a\) , \( -\frac{23}{2} a^{5} + \frac{13}{2} a^{4} + \frac{221}{2} a^{3} - 68 a^{2} - 232 a + 149\) , \( -\frac{403}{4} a^{5} + \frac{127}{2} a^{4} + \frac{1931}{2} a^{3} - 608 a^{2} - 2028 a + 1275\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-2a+1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{5}{2}a^{3}-7a-1\right){x}^{2}+\left(-\frac{23}{2}a^{5}+\frac{13}{2}a^{4}+\frac{221}{2}a^{3}-68a^{2}-232a+149\right){x}-\frac{403}{4}a^{5}+\frac{127}{2}a^{4}+\frac{1931}{2}a^{3}-608a^{2}-2028a+1275$ |
| 392.1-m1 |
392.1-m |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.004022561$ |
$19423.78053$ |
6.34232 |
\( \frac{5956547}{56} a^{5} + \frac{2292172333}{392} a^{4} + \frac{2228890201}{392} a^{3} - \frac{1241205775}{28} a^{2} - \frac{2029087150}{49} a + \frac{4045133821}{98} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + \frac{5}{2} a^{3} + a^{2} - 5 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 4 a - 1\) , \( \frac{3}{2} a^{4} - \frac{1}{2} a^{3} - \frac{15}{2} a^{2} + 2 a + 9\) , \( \frac{13}{4} a^{5} + \frac{7}{2} a^{4} - 30 a^{3} - 23 a^{2} + 61 a + 39\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a+2\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+4a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+\frac{5}{2}a^{3}+a^{2}-5a\right){x}^{2}+\left(\frac{3}{2}a^{4}-\frac{1}{2}a^{3}-\frac{15}{2}a^{2}+2a+9\right){x}+\frac{13}{4}a^{5}+\frac{7}{2}a^{4}-30a^{3}-23a^{2}+61a+39$ |
*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.
