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 |
273.2-a2 |
273.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.2 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{12} \cdot 7^{4} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (-3a+1), (4a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.774212068$ |
0.682894543 |
\( \frac{7478174461}{842751} a - \frac{150471620027}{22754277} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24 a - 15\) , \( 36 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a-15\right){x}+36a-9$ |
273.2-a8 |
273.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.2 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{4} \cdot 7^{12} \cdot 13^{3} \) |
$0.62913$ |
$(-2a+1), (-3a+1), (4a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.591404022$ |
0.682894543 |
\( -\frac{12174283995544342099}{273683771825373} a + \frac{1235018026428367060}{30409307980597} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -111 a - 195\) , \( 837 a + 1080\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-111a-195\right){x}+837a+1080$ |
273.3-a2 |
273.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.3 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{12} \cdot 7^{4} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.774212068$ |
0.682894543 |
\( -\frac{7478174461}{842751} a + \frac{51439090420}{22754277} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -24 a + 10\) , \( -51 a + 51\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a+10\right){x}-51a+51$ |
273.3-a8 |
273.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.3 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{4} \cdot 7^{12} \cdot 13^{3} \) |
$0.62913$ |
$(-2a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.591404022$ |
0.682894543 |
\( \frac{12174283995544342099}{273683771825373} a - \frac{1059121757689038559}{273683771825373} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 111 a - 305\) , \( -1032 a + 1806\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(111a-305\right){x}-1032a+1806$ |
300.1-a1 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.294290140$ |
0.747258760 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
300.1-a2 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.882870421$ |
0.747258760 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( a - 2\) , \( 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-2\right){x}+2$ |
14196.2-f3 |
14196.2-f |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14196.2 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{6} \cdot 13^{4} \) |
$1.68943$ |
$(-2a+1), (-3a+1), (-4a+1), (4a-3), (2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.297286955$ |
2.059664444 |
\( \frac{13114301472005393}{297763030656} a - \frac{1022733290806164619}{9528416980992} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -913 a + 1382\) , \( 9312 a + 10425\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-913a+1382\right){x}+9312a+10425$ |
14196.2-f6 |
14196.2-f |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14196.2 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \cdot 13^{4} \) |
$1.68943$ |
$(-2a+1), (-3a+1), (-4a+1), (4a-3), (2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.891860865$ |
2.059664444 |
\( \frac{35254619411}{139518288} a + \frac{66721467262}{78479037} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 32 a - 58\) , \( 60 a + 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(32a-58\right){x}+60a+48$ |
14196.5-f3 |
14196.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14196.5 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{6} \cdot 13^{4} \) |
$1.68943$ |
$(-2a+1), (3a-2), (-4a+1), (4a-3), (2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.297286955$ |
2.059664444 |
\( -\frac{13114301472005393}{297763030656} a - \frac{201025214567330681}{3176138993664} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 469 a - 1382\) , \( -9312 a + 19737\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(469a-1382\right){x}-9312a+19737$ |
14196.5-f6 |
14196.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14196.5 |
\( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \cdot 13^{4} \) |
$1.68943$ |
$(-2a+1), (3a-2), (-4a+1), (4a-3), (2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.891860865$ |
2.059664444 |
\( -\frac{35254619411}{139518288} a + \frac{1384835050891}{1255664592} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -26 a + 58\) , \( -60 a + 108\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a+58\right){x}-60a+108$ |
14700.2-i1 |
14700.2-i |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14700.2 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 7^{24} \) |
$1.70423$ |
$(-2a+1), (-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{8} \cdot 3^{3} \) |
$1$ |
$0.049562042$ |
2.747007217 |
\( -\frac{932348627918877961}{358766164249920} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 20352 a\) , \( -1443724\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+20352a{x}-1443724$ |
14700.2-i2 |
14700.2-i |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14700.2 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 5^{6} \cdot 7^{8} \) |
$1.70423$ |
$(-2a+1), (-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{8} \cdot 3^{2} \) |
$1$ |
$0.148686127$ |
2.747007217 |
\( \frac{785793873833639}{637994920500} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -1923 a\) , \( 20756\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-1923a{x}+20756$ |
650.3-a2 |
650.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.3 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{5} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.892849288$ |
1.446424644 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -2 i - 1\) , \( 3 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-2i-1\right){x}+3i+4$ |
650.3-a4 |
650.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.3 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{3} \cdot 5^{14} \cdot 13^{4} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.723212322$ |
1.446424644 |
\( -\frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 108 i + 9\) , \( -171 i - 274\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(108i+9\right){x}-171i-274$ |
650.4-a2 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{5} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.892849288$ |
1.446424644 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( i - 1\) , \( -4 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}-4i+4$ |
650.4-a4 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{3} \cdot 5^{14} \cdot 13^{4} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.723212322$ |
1.446424644 |
\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -109 i + 9\) , \( 170 i - 274\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-109i+9\right){x}+170i-274$ |
4050.2-c1 |
4050.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4050.2 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{6} \) |
$1.42571$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.431430046$ |
2.588580280 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$ |
4050.2-c3 |
4050.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4050.2 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{14} \cdot 5^{24} \) |
$1.42571$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{3} \) |
$1$ |
$0.107857511$ |
2.588580280 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4082{x}+14681$ |
8450.5-a4 |
8450.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.5 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 5^{15} \cdot 13^{5} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.170464153$ |
$0.473037374$ |
2.214693161 |
\( -\frac{321714644118649477}{13945800781250} a + \frac{162841521219476968}{6972900390625} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -370 i + 148\) , \( 732 i - 2932\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-370i+148\right){x}+732i-2932$ |
8450.5-a5 |
8450.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.5 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 5^{15} \cdot 13^{5} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.170464153$ |
$0.473037374$ |
2.214693161 |
\( \frac{321714644118649477}{13945800781250} a + \frac{162841521219476968}{6972900390625} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 370 i + 148\) , \( -732 i - 2932\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(370i+148\right){x}-732i-2932$ |
22050.2-b2 |
22050.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 5^{6} \cdot 7^{8} \) |
$2.17781$ |
$(a+1), (-a-2), (2a+1), (3), (7)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1.696399518$ |
$0.148686127$ |
3.026772894 |
\( \frac{785793873833639}{637994920500} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 1923\) , \( -20756\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+1923{x}-20756$ |
22050.2-b5 |
22050.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{24} \cdot 7^{2} \) |
$2.17781$ |
$(a+1), (-a-2), (2a+1), (3), (7)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1.696399518$ |
$0.148686127$ |
3.026772894 |
\( \frac{9150443179640281}{184570312500} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -4357\) , \( 109132\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-4357{x}+109132$ |
39650.5-g1 |
39650.5-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
39650.5 |
\( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) |
\( 2^{3} \cdot 5^{18} \cdot 13 \cdot 61^{4} \) |
$2.52191$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (-6a-5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.144205299$ |
3.460927196 |
\( \frac{76911185482379738283023}{175777278320312500} a - \frac{17069327857089274127939}{175777278320312500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 962 i - 6628\) , \( 44990 i - 206754\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(962i-6628\right){x}+44990i-206754$ |
39650.5-g6 |
39650.5-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
39650.5 |
\( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{4} \cdot 61 \) |
$2.52191$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (-6a-5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.576821199$ |
3.460927196 |
\( \frac{1036917664614083}{217777625000} a + \frac{8700158718205027}{1742221000000} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 132 i + 143\) , \( -333 i + 888\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(132i+143\right){x}-333i+888$ |
39650.8-g1 |
39650.8-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
39650.8 |
\( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) |
\( 2^{3} \cdot 5^{18} \cdot 13 \cdot 61^{4} \) |
$2.52191$ |
$(a+1), (-a-2), (2a+1), (2a+3), (5a+6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.144205299$ |
3.460927196 |
\( -\frac{76911185482379738283023}{175777278320312500} a - \frac{17069327857089274127939}{175777278320312500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -963 i - 6628\) , \( -44991 i - 206754\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-963i-6628\right){x}-44991i-206754$ |
39650.8-g6 |
39650.8-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
39650.8 |
\( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{4} \cdot 61 \) |
$2.52191$ |
$(a+1), (-a-2), (2a+1), (2a+3), (5a+6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.576821199$ |
3.460927196 |
\( -\frac{1036917664614083}{217777625000} a + \frac{8700158718205027}{1742221000000} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( -133 i + 143\) , \( 332 i + 888\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-133i+143\right){x}+332i+888$ |
68450.5-h1 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{15} \cdot 37^{5} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.207070166$ |
4.969683988 |
\( -\frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -920 i + 2805\) , \( 54952 i + 28239\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-920i+2805\right){x}+54952i+28239$ |
68450.5-h2 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{15} \cdot 37^{5} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.207070166$ |
4.969683988 |
\( \frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 920 i + 2805\) , \( -54952 i + 28239\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(920i+2805\right){x}-54952i+28239$ |
44.3-a3 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{2222449}{45056} a + \frac{42043605}{45056} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$ |
44.4-a3 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( -\frac{2222449}{45056} a + \frac{22133027}{22528} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}+1$ |
644.3-b6 |
644.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
644.3 |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 7^{4} \cdot 23 \) |
$1.19099$ |
$(a), (-a+1), (-2a+1), (-2a+5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$1.883441247$ |
2.847495514 |
\( -\frac{9858228523}{4616192} a + \frac{2914425481}{4616192} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -11 a + 6\) , \( -17 a + 30\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-11a+6\right){x}-17a+30$ |
644.4-b6 |
644.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
644.4 |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{18} \cdot 7^{4} \cdot 23 \) |
$1.19099$ |
$(a), (-a+1), (-2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$1.883441247$ |
2.847495514 |
\( \frac{9858228523}{4616192} a - \frac{3471901521}{2308096} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 10 a - 5\) , \( 16 a + 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-5\right){x}+16a+13$ |
2772.3-c2 |
2772.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2772.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \) |
\( 2^{28} \cdot 3^{6} \cdot 7^{4} \cdot 11 \) |
$1.71548$ |
$(a), (-a+1), (-2a+1), (-2a+3), (3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.645013956$ |
1.950338880 |
\( \frac{482697730182277}{244158824448} a - \frac{330906907974815}{122079412224} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 63 a + 63\) , \( 135 a - 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(63a+63\right){x}+135a-621$ |
2772.4-d2 |
2772.4-d |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2772.4 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \) |
\( 2^{28} \cdot 3^{6} \cdot 7^{4} \cdot 11 \) |
$1.71548$ |
$(a), (-a+1), (-2a+1), (2a+1), (3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.645013956$ |
1.950338880 |
\( -\frac{482697730182277}{244158824448} a - \frac{8529337417493}{11626610688} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -63 a + 126\) , \( -135 a - 486\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-63a+126\right){x}-135a-486$ |
6300.2-b2 |
6300.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6300.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{24} \cdot 5^{6} \cdot 7^{8} \) |
$2.10631$ |
$(a), (-a+1), (-2a+1), (3), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{2} \) |
$1$ |
$0.148686127$ |
0.899169179 |
\( \frac{785793873833639}{637994920500} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1922{x}+20756$ |
6300.2-d3 |
6300.2-d |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6300.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{6} \cdot 5^{2} \cdot 7^{2} \) |
$2.10631$ |
$(a), (-a+1), (-2a+1), (3), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$1.090738100$ |
4.947123017 |
\( \frac{7633736209}{3870720} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -41\) , \( -39\bigr] \) |
${y}^2+{x}{y}={x}^{3}-41{x}-39$ |
8100.2-b1 |
8100.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{6} \) |
$2.24289$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1$ |
$0.431430046$ |
3.913565526 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$ |
108.2-a8 |
108.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
108.2 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{19} \) |
$0.81478$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.488316936$ |
1.052398998 |
\( \frac{715706108}{531441} a + \frac{421307996}{531441} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 13 a + 37\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+13a+37$ |
108.3-a7 |
108.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
108.3 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{19} \) |
$0.81478$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.488316936$ |
1.052398998 |
\( -\frac{715706108}{531441} a + \frac{421307996}{531441} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -13 a + 37\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-21\right){x}-13a+37$ |
450.2-a4 |
450.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.16409$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.970717605$ |
1.372802002 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
594.3-c6 |
594.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
594.3 |
\( 2 \cdot 3^{3} \cdot 11 \) |
\( 2^{12} \cdot 3^{13} \cdot 11 \) |
$1.24776$ |
$(a), (-a-1), (a-1), (a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$1.704113391$ |
2.409980269 |
\( -\frac{84007489}{128304} a + \frac{468710027}{513216} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 9 a + 4\) , \( -4 a + 27\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+4\right){x}-4a+27$ |
594.6-c6 |
594.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
594.6 |
\( 2 \cdot 3^{3} \cdot 11 \) |
\( 2^{12} \cdot 3^{13} \cdot 11 \) |
$1.24776$ |
$(a), (-a-1), (a-1), (a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$1.704113391$ |
2.409980269 |
\( \frac{84007489}{128304} a + \frac{468710027}{513216} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9 a + 4\) , \( 4 a + 27\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a+4\right){x}+4a+27$ |
4050.3-c1 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{2} \) |
$0.940639818$ |
$0.431430046$ |
4.591332359 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$ |
7524.5-c2 |
7524.5-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7524.5 |
\( 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \) |
\( 2^{8} \cdot 3^{18} \cdot 11 \cdot 19^{4} \) |
$2.35394$ |
$(a), (-a-1), (a-1), (a+3), (-3a+1)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1.393610825$ |
$0.433086737$ |
5.121328620 |
\( -\frac{9232718736054548}{761837148171} a - \frac{17532010176936668}{761837148171} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 63 a - 452\) , \( 828 a - 3639\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(63a-452\right){x}+828a-3639$ |
7524.8-c2 |
7524.8-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7524.8 |
\( 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \) |
\( 2^{8} \cdot 3^{18} \cdot 11 \cdot 19^{4} \) |
$2.35394$ |
$(a), (-a-1), (a-1), (a-3), (3a+1)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$1.393610825$ |
$0.433086737$ |
5.121328620 |
\( \frac{9232718736054548}{761837148171} a - \frac{17532010176936668}{761837148171} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -63 a - 452\) , \( -828 a - 3639\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-63a-452\right){x}-828a-3639$ |
10098.8-j6 |
10098.8-j |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10098.8 |
\( 2 \cdot 3^{3} \cdot 11 \cdot 17 \) |
\( 2^{12} \cdot 3^{21} \cdot 11 \cdot 17^{3} \) |
$2.53363$ |
$(a), (-a-1), (a-1), (a-3), (2a+3)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$0.996659843$ |
$0.408314069$ |
6.906174528 |
\( \frac{68070478181263}{229765327704} a + \frac{394438305984299}{1838122621632} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 112 a - 97\) , \( 849 a - 1385\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(112a-97\right){x}+849a-1385$ |
10098.9-i6 |
10098.9-i |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10098.9 |
\( 2 \cdot 3^{3} \cdot 11 \cdot 17 \) |
\( 2^{12} \cdot 3^{21} \cdot 11 \cdot 17^{3} \) |
$2.53363$ |
$(a), (-a-1), (a-1), (a+3), (-2a+3)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$0.996659843$ |
$0.408314069$ |
6.906174528 |
\( -\frac{68070478181263}{229765327704} a + \frac{394438305984299}{1838122621632} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -112 a - 97\) , \( -849 a - 1385\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-112a-97\right){x}-849a-1385$ |
22050.2-b2 |
22050.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 5^{6} \cdot 7^{8} \) |
$3.07989$ |
$(a), (-a-1), (a-1), (5), (7)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{3} \) |
$1.029804775$ |
$0.148686127$ |
5.196986521 |
\( \frac{785793873833639}{637994920500} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1922{x}+20756$ |
22050.2-e1 |
22050.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 5^{8} \cdot 7^{2} \) |
$3.07989$ |
$(a), (-a-1), (a-1), (5), (7)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{3} \) |
$1$ |
$0.272684525$ |
4.627609845 |
\( -\frac{58818484369}{18600435000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -81\) , \( 6561\bigr] \) |
${y}^2+{x}{y}={x}^{3}-81{x}+6561$ |
7425.5-h8 |
7425.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{15} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1.407799633$ |
$0.256794058$ |
5.232035875 |
\( -\frac{1032777340820292487}{1427209716796875} a + \frac{1521986905848333643}{475736572265625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -138 a + 853\) , \( -2710 a - 2479\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-138a+853\right){x}-2710a-2479$ |
*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.