| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$1.64041$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$22.42699724$ |
2.748771867 |
\( -1458 a + 14121 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 43 a - 416\) , \( 439 a - 4249\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(43a-416\right){x}+439a-4249$ |
| 1.1-a2 |
1.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$1.64041$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$22.42699724$ |
2.748771867 |
\( 1458 a + 12663 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -43 a - 373\) , \( -439 a - 3810\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-43a-373\right){x}-439a-3810$ |
| 4.1-a1 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.280047816$ |
0.793138948 |
\( -\frac{82163961}{262144} a - \frac{162174691}{262144} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 12198943922868379 a - 118070892941095154\) , \( -936790687705518244827671 a + 9066990855572814480621272\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(12198943922868379a-118070892941095154\right){x}-936790687705518244827671a+9066990855572814480621272$ |
| 4.1-a2 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.280047816$ |
0.793138948 |
\( -\frac{528261921}{512} a + \frac{1278413521}{128} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4762705849 a + 41334475675\) , \( 256146802376611 a + 2223041713599569\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4762705849a+41334475675\right){x}+256146802376611a+2223041713599569$ |
| 4.1-a3 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.280047816$ |
0.793138948 |
\( \frac{82163961}{262144} a - \frac{61084663}{65536} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -12198943922868379 a - 105871949018226775\) , \( 936790687705518244827671 a + 8130200167867296235793601\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-12198943922868379a-105871949018226775\right){x}+936790687705518244827671a+8130200167867296235793601$ |
| 4.1-a4 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.280047816$ |
0.793138948 |
\( \frac{528261921}{512} a + \frac{4585392163}{512} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4762705849 a + 46097181524\) , \( -256146802376611 a + 2479188515976180\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-4762705849a+46097181524\right){x}-256146802376611a+2479188515976180$ |
| 4.1-b1 |
4.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.296357500$ |
$24.24844773$ |
2.348746609 |
\( -\frac{32011221}{8} a - 34727327 \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 107955 a - 1044877\) , \( 418588924 a - 4051430077\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(107955a-1044877\right){x}+418588924a-4051430077$ |
| 4.1-b2 |
4.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.098785833$ |
$24.24844773$ |
2.348746609 |
\( -\frac{1881}{512} a + \frac{263}{128} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -16 a - 134\) , \( 723 a + 6256\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-16a-134\right){x}+723a+6256$ |
| 4.1-c1 |
4.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.296357500$ |
$24.24844773$ |
2.348746609 |
\( \frac{32011221}{8} a - \frac{309829837}{8} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -107956 a - 936922\) , \( -418588925 a - 3632841153\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-107956a-936922\right){x}-418588925a-3632841153$ |
| 4.1-c2 |
4.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$2.31990$ |
$(3a+26), (3a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.098785833$ |
$24.24844773$ |
2.348746609 |
\( \frac{1881}{512} a - \frac{829}{512} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 15 a - 150\) , \( -724 a + 6979\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-150\right){x}-724a+6979$ |
| 6.2-a1 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{26} \cdot 3^{4} \) |
$2.56739$ |
$(3a+26), (-28a+271)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.812886755$ |
$7.178122080$ |
5.963617601 |
\( -\frac{1362129212829017}{5435817984} a + \frac{4397484313013503}{1811939328} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 21521911351567 a + 186783931116931\) , \( 46324736211976883448 a + 402042188367073909097\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(21521911351567a+186783931116931\right){x}+46324736211976883448a+402042188367073909097$ |
| 6.2-a2 |
6.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \) |
$2.56739$ |
$(3a+26), (-28a+271)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.625773511$ |
$14.35624416$ |
5.963617601 |
\( -\frac{85019010917577481}{73728} a + \frac{274293430675992527}{24576} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 6083036276474164986 a - 58876369093719015841\) , \( -24742079501273165104881755104 a + 239473141151057045098076553321\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6083036276474164986a-58876369093719015841\right){x}-24742079501273165104881755104a+239473141151057045098076553321$ |
| 6.2-b1 |
6.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{2} \) |
$2.56739$ |
$(3a+26), (-28a+271)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$46.36527657$ |
3.788516328 |
\( -\frac{66834649}{72} a + \frac{215684951}{24} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 1383572054 a - 13391289334\) , \( -84861911528508 a + 821359761485203\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1383572054a-13391289334\right){x}-84861911528508a+821359761485203$ |
| 6.2-b2 |
6.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$2.56739$ |
$(3a+26), (-28a+271)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$46.36527657$ |
3.788516328 |
\( \frac{26184277}{192} a + \frac{75529629}{64} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 747343578529169 a - 7233373987834856\) , \( -41315722738160942113139 a + 399885785773359581028121\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(747343578529169a-7233373987834856\right){x}-41315722738160942113139a+399885785773359581028121$ |
| 6.3-a1 |
6.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{26} \cdot 3^{4} \) |
$2.56739$ |
$(3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.812886755$ |
$7.178122080$ |
5.963617601 |
\( \frac{1362129212829017}{5435817984} a + \frac{2957580931552873}{1358954496} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -21521911351568 a + 208305842468498\) , \( -46324736211976883449 a + 448366924579050792545\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-21521911351568a+208305842468498\right){x}-46324736211976883449a+448366924579050792545$ |
| 6.3-a2 |
6.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \) |
$2.56739$ |
$(3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.625773511$ |
$14.35624416$ |
5.963617601 |
\( \frac{85019010917577481}{73728} a + \frac{184465320277600025}{18432} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -6083036276474164987 a - 52793332817244850855\) , \( 24742079501273165104881755103 a + 214731061649783879993194798217\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-6083036276474164987a-52793332817244850855\right){x}+24742079501273165104881755103a+214731061649783879993194798217$ |
| 6.3-b1 |
6.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$2.56739$ |
$(3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$46.36527657$ |
3.788516328 |
\( -\frac{26184277}{192} a + \frac{63193291}{48} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -747343578529170 a - 6486030409305686\) , \( 41315722738160942113138 a + 358570063035198638914983\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-747343578529170a-6486030409305686\right){x}+41315722738160942113138a+358570063035198638914983$ |
| 6.3-b2 |
6.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{2} \) |
$2.56739$ |
$(3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$46.36527657$ |
3.788516328 |
\( \frac{66834649}{72} a + \frac{145055051}{18} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -1383572055 a - 12007717279\) , \( 84861911528507 a + 736497849956696\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-1383572055a-12007717279\right){x}+84861911528507a+736497849956696$ |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$2.66826$ |
$(-688a-5971)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.112226249$ |
$34.86649664$ |
0.852604859 |
\( -\frac{5971968}{343} a + \frac{57839616}{343} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 110671282 a - 1071162977\) , \( -1914834524762 a + 18533261862878\bigr] \) |
${y}^2+{y}={x}^{3}+\left(110671282a-1071162977\right){x}-1914834524762a+18533261862878$ |
| 7.2-a1 |
7.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$2.66826$ |
$(688a-6659)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.112226249$ |
$34.86649664$ |
0.852604859 |
\( \frac{5971968}{343} a + \frac{7409664}{49} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -110671282 a - 960491695\) , \( 1914834524762 a + 16618427338116\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-110671282a-960491695\right){x}+1914834524762a+16618427338116$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.84128$ |
$(-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$3.196710357$ |
$20.95136323$ |
3.648384685 |
\( -1458 a + 14121 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4\) , \( 7 a + 46\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+4{x}+7a+46$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.84128$ |
$(-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.598355178$ |
$20.95136323$ |
3.648384685 |
\( 1458 a + 12663 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -11360686 a - 98596889\) , \( 61079506336 a + 530095590370\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-11360686a-98596889\right){x}+61079506336a+530095590370$ |
| 9.3-a1 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.84128$ |
$(-28a+271)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.598355178$ |
$20.95136323$ |
3.648384685 |
\( -1458 a + 14121 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 11360685 a - 109957574\) , \( -61079506337 a + 591175096707\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(11360685a-109957574\right){x}-61079506337a+591175096707$ |
| 9.3-a2 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.84128$ |
$(-28a+271)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$3.196710357$ |
$20.95136323$ |
3.648384685 |
\( 1458 a + 12663 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a + 5\) , \( -8 a + 54\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+5\right){x}-8a+54$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3 \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$14.14375370$ |
1.540918716 |
\( -\frac{1541}{192} a + \frac{53363}{48} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -2 a + 49\) , \( -6 a + 27\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-2a+49\right){x}-6a+27$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{2} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$28.28750740$ |
1.540918716 |
\( \frac{1207}{72} a + \frac{94399}{36} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 6106004 a - 59098639\) , \( 13698903656 a - 132588673051\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(6106004a-59098639\right){x}+13698903656a-132588673051$ |
| 12.1-b1 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{12} \cdot 3^{12} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.244356124$ |
$9.412688674$ |
1.701422477 |
\( \frac{1721004361}{17006112} a + \frac{27284443207}{34012224} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -4865220300748 a - 42224176035242\) , \( 3071845681160915820 a + 26659872477818388380\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-4865220300748a-42224176035242\right){x}+3071845681160915820a+26659872477818388380$ |
| 12.1-b2 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{45} \cdot 3^{2} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$7.466136744$ |
$2.091708594$ |
1.701422477 |
\( -\frac{175169947246561}{618475290624} a + \frac{7178498567624101}{618475290624} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -27494272 a - 238616735\) , \( -213326491008 a - 1851413657038\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-27494272a-238616735\right){x}-213326491008a-1851413657038$ |
| 12.1-b3 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{6} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.488712248$ |
$18.82537734$ |
1.701422477 |
\( \frac{42049922063}{2985984} a + \frac{1146422347765}{2985984} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -6348072 a - 55093520\) , \( 26332200832 a + 228531374654\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-6348072a-55093520\right){x}+26332200832a+228531374654$ |
| 12.1-b4 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{36} \cdot 3^{4} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$3.733068372$ |
$1.045854297$ |
1.701422477 |
\( \frac{37915139761129}{10616832} a + \frac{658115869962439}{21233664} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -244986486707468 a - 2126183790567737\) , \( -6323580637967408477036 a - 54880964380899622414948\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-244986486707468a-2126183790567737\right){x}-6323580637967408477036a-54880964380899622414948$ |
| 12.1-c1 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{24} \cdot 3^{3} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 11 \) |
$0.344625497$ |
$7.128565437$ |
8.832395993 |
\( -\frac{3072738109}{113246208} a + \frac{53840373619}{28311552} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 7098 a + 61602\) , \( 230272 a + 1998480\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(7098a+61602\right){x}+230272a+1998480$ |
| 12.1-c2 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{6} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 11 \) |
$0.172312748$ |
$7.128565437$ |
8.832395993 |
\( -\frac{120229554767}{1492992} a + \frac{291598526561}{373248} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 162 a - 1568\) , \( 3412 a - 33024\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(162a-1568\right){x}+3412a-33024$ |
| 12.1-d1 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{17} \cdot 3^{16} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 7 \) |
$1$ |
$1.933792420$ |
3.686913491 |
\( \frac{659491076418671}{44079842304} a + \frac{7882751939698333}{44079842304} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -3057233 a - 26533030\) , \( -8803103504 a - 76400197561\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3057233a-26533030\right){x}-8803103504a-76400197561$ |
| 12.1-d2 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{19} \cdot 3^{8} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \cdot 7 \) |
$1$ |
$1.933792420$ |
3.686913491 |
\( \frac{610502953353695353}{107495424} a + \frac{1324605250758468617}{26873856} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -28028774474109 a - 243255563836400\) , \( -244715754802786639602 a - 2123834167961774675371\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-28028774474109a-243255563836400\right){x}-244715754802786639602a-2123834167961774675371$ |
| 12.1-e1 |
12.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{5} \cdot 3 \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$18.15555386$ |
3.955984152 |
\( -\frac{25755149}{48} a + \frac{62302817}{12} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 6170158830 a - 59719609077\) , \( 799196730265370 a - 7735249229332299\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6170158830a-59719609077\right){x}+799196730265370a-7735249229332299$ |
| 12.1-e2 |
12.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{4} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$36.31110772$ |
3.955984152 |
\( -\frac{1130353}{1296} a + \frac{14695165}{1296} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -9384297579290 a - 81444252975349\) , \( 30116822588108775710 a + 261377273786951205983\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9384297579290a-81444252975349\right){x}+30116822588108775710a+261377273786951205983$ |
| 12.1-e3 |
12.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$36.31110772$ |
3.955984152 |
\( \frac{2062802}{9} a + \frac{71752513}{36} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3809411512637748 a - 36870455485417793\) , \( 290730865947531567946536 a - 2813920054473985765035121\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3809411512637748a-36870455485417793\right){x}+290730865947531567946536a-2813920054473985765035121$ |
| 12.1-e4 |
12.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$18.15555386$ |
3.955984152 |
\( \frac{2897525342222}{3} a + \frac{50293969260785}{6} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -9313736776399012 a + 90145608075651937\) , \( 1855074380374920468511678 a - 17954856580036998090455725\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9313736776399012a+90145608075651937\right){x}+1855074380374920468511678a-17954856580036998090455725$ |
| 12.1-f1 |
12.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{25} \cdot 3^{4} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 7 \) |
$0.087402750$ |
$9.547685012$ |
11.45536085 |
\( -\frac{71129698745879}{21233664} a + \frac{172121601314297}{5308416} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 11625209635080 a - 112517845062630\) , \( -65365779860492102119 a + 632660994649825822176\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(11625209635080a-112517845062630\right){x}-65365779860492102119a+632660994649825822176$ |
| 12.1-f2 |
12.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{23} \cdot 3^{8} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
$0.043701375$ |
$9.547685012$ |
11.45536085 |
\( \frac{935448061703}{107495424} a + \frac{9044234871613}{107495424} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 6870434109710819476 a - 66497419395938559740\) , \( -26551956998745047083051956341 a + 256990547050423884224601543852\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(6870434109710819476a-66497419395938559740\right){x}-26551956998745047083051956341a+256990547050423884224601543852$ |
| 12.1-g1 |
12.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{35} \cdot 3^{7} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 7 \) |
$1$ |
$3.591167639$ |
2.738727131 |
\( -\frac{107468052580541}{37572373905408} a - \frac{233158806713869}{9393093476352} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -8781 a + 85019\) , \( -1456698071 a + 14099059943\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-8781a+85019\right){x}-1456698071a+14099059943$ |
| 12.1-g2 |
12.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{19} \cdot 3^{14} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$7.182335279$ |
2.738727131 |
\( \frac{5590974660021577}{626913312768} a + \frac{20265650109455705}{156728328192} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 4159858757473 a - 40262357226069\) , \( -13756906446391226173 a + 133150069260306542193\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(4159858757473a-40262357226069\right){x}-13756906446391226173a+133150069260306542193$ |
| 12.1-h1 |
12.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.756399195$ |
$13.36507900$ |
4.405524544 |
\( \frac{63145}{162} a + \frac{1096039}{324} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -181030 a - 1571092\) , \( -111226110 a - 965306962\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-181030a-1571092\right){x}-111226110a-965306962$ |
| 12.1-h2 |
12.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{2} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.512798391$ |
$26.73015800$ |
4.405524544 |
\( -\frac{389017}{144} a + \frac{5057221}{144} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 26\) , \( 2 a - 16\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+26{x}+2a-16$ |
| 12.1-i1 |
12.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{32} \cdot 3^{4} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.607673348$ |
0.719885806 |
\( -\frac{2909156689865}{21743271936} a + \frac{21487704655661}{21743271936} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1586557172119876133 a - 15355937628594813932\) , \( -1459285073817053601303191656 a + 14124099004848790760901929616\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1586557172119876133a-15355937628594813932\right){x}-1459285073817053601303191656a+14124099004848790760901929616$ |
| 12.1-i2 |
12.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{22} \cdot 3^{8} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.607673348$ |
0.719885806 |
\( \frac{4195435722425}{107495424} a + \frac{36559509979747}{107495424} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -611469563735 a + 5918279307898\) , \( -396615197484523422 a + 3838751191668359124\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-611469563735a+5918279307898\right){x}-396615197484523422a+3838751191668359124$ |
| 12.1-j1 |
12.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{19} \cdot 3 \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$9.217834091$ |
9.038293536 |
\( -\frac{84872309}{786432} a + \frac{203925179}{196608} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -503997 a - 4374079\) , \( -9082997998 a - 78829340233\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-503997a-4374079\right){x}-9082997998a-78829340233$ |
| 12.1-j2 |
12.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$9.217834091$ |
9.038293536 |
\( -\frac{2540903189}{1728} a + \frac{6148213817}{432} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 277 a - 2681\) , \( 7718 a - 74701\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(277a-2681\right){x}+7718a-74701$ |
| 12.1-j3 |
12.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{6} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$18.43566818$ |
9.038293536 |
\( \frac{56577263}{46656} a + \frac{769938397}{46656} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 166187953 a - 1608496615\) , \( 2979091110318 a - 28833967085359\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(166187953a-1608496615\right){x}+2979091110318a-28833967085359$ |
| 12.1-j4 |
12.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{337}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{2} \) |
$3.05315$ |
$(3a+26), (3a-29), (-28a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$18.43566818$ |
9.038293536 |
\( -\frac{231009263}{4608} a + \frac{683871425}{1152} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3 a - 27\) , \( -10 a - 87\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3a-27\right){x}-10a-87$ |
*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.
