| 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 |
| 108.6-a1 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{22} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( \frac{114244921}{432} a - \frac{21056689}{108} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 45 a + 174\) , \( 461 a - 1226\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(45a+174\right){x}+461a-1226$ |
| 108.6-a2 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{22} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.209276533$ |
2.017212702 |
\( \frac{32836083791}{4251528} a - \frac{26111762207}{708588} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 34 a - 252\) , \( -340 a + 1624\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(34a-252\right){x}-340a+1624$ |
| 108.6-a3 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{4} \cdot 3^{22} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.209276533$ |
2.017212702 |
\( -\frac{32836083791}{4251528} a - \frac{123834489451}{4251528} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 12 a - 63\) , \( -74 a + 161\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(12a-63\right){x}-74a+161$ |
| 108.6-a4 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{14} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( \frac{8592493}{46656} a - \frac{398467}{7776} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -6 a - 12\) , \( -28 a + 40\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-6a-12\right){x}-28a+40$ |
| 108.6-a5 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( -\frac{8592493}{46656} a + \frac{6201691}{46656} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2 a - 3\) , \( 5\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(2a-3\right){x}+5$ |
| 108.6-a6 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{10} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( \frac{250499417}{110592} a + \frac{273138433}{110592} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -14 a + 36\) , \( 26 a + 76\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-14a+36\right){x}+26a+76$ |
| 108.6-a7 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{10} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( -\frac{250499417}{110592} a + \frac{87272975}{18432} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 9\) , \( -2 a - 1\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+9{x}-2a-1$ |
| 108.6-a8 |
108.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{10} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.418553067$ |
2.017212702 |
\( -\frac{114244921}{432} a + \frac{10006055}{144} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 38 a - 57\) , \( -193 a - 129\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(38a-57\right){x}-193a-129$ |
| 108.6-b1 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{15} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.273865281$ |
$1.065785020$ |
1.947568094 |
\( \frac{69084352753}{104976} a - \frac{1402170891281}{34992} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -23 a + 894\) , \( -3847 a + 802\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-23a+894\right){x}-3847a+802$ |
| 108.6-b2 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{6} \cdot 3^{15} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.547730562$ |
$1.065785020$ |
1.947568094 |
\( -\frac{69084352753}{104976} a - \frac{2068714160545}{52488} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -63 a + 190\) , \( 193 a + 871\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-63a+190\right){x}+193a+871$ |
| 108.6-b3 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{12} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.136932640$ |
$2.131570041$ |
1.947568094 |
\( \frac{54256267}{20736} a - \frac{3034703}{6912} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -3 a + 54\) , \( -43 a + 10\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-3a+54\right){x}-43a+10$ |
| 108.6-b4 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{30} \cdot 3^{9} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.547730562$ |
$2.131570041$ |
1.947568094 |
\( \frac{134585581}{589824} a - \frac{111715025}{294912} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 23\) , \( 37 a + 83\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-4a-23\right){x}+37a+83$ |
| 108.6-b5 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{30} \cdot 3^{9} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.068466320$ |
$2.131570041$ |
1.947568094 |
\( -\frac{134585581}{589824} a - \frac{29614823}{196608} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 34\) , \( -39 a - 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-3a+34\right){x}-39a-73$ |
| 108.6-b6 |
108.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.273865281$ |
$2.131570041$ |
1.947568094 |
\( -\frac{54256267}{20736} a + \frac{22576079}{10368} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -3 a + 10\) , \( a + 7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-3a+10\right){x}+a+7$ |
| 108.6-c1 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{17} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$0.602842775$ |
2.011222529 |
\( \frac{109951540241875}{419904} a - \frac{33314367587125}{69984} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -855 a + 3588\) , \( 24741 a + 54133\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-855a+3588\right){x}+24741a+54133$ |
| 108.6-c2 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{17} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.602842775$ |
2.011222529 |
\( -\frac{109951540241875}{419904} a - \frac{89934665280875}{419904} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -96 a + 958\) , \( -4007 a - 1907\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-96a+958\right){x}-4007a-1907$ |
| 108.6-c3 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{25} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( \frac{354186588125}{186624} a - \frac{27812478875}{31104} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -38 a - 1175\) , \( 758 a + 15755\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-38a-1175\right){x}+758a+15755$ |
| 108.6-c4 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{23} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( \frac{368445625}{452984832} a - \frac{2494870375}{50331648} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -38 a + 40\) , \( 353 a - 2065\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-38a+40\right){x}+353a-2065$ |
| 108.6-c5 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( -\frac{368445625}{452984832} a - \frac{11042693875}{226492416} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4 a - 2\) , \( 13 a + 55\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(4a-2\right){x}+13a+55$ |
| 108.6-c6 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{17} \cdot 3^{31} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.602842775$ |
2.011222529 |
\( \frac{619619905802875}{2259436291848} a + \frac{216583694696500}{282429536481} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 57 a + 394\) , \( 459 a - 4141\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(57a+394\right){x}+459a-4141$ |
| 108.6-c7 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{17} \cdot 3^{31} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.602842775$ |
2.011222529 |
\( -\frac{619619905802875}{2259436291848} a + \frac{784096487791625}{753145430616} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 42 a - 461\) , \( 1149 a - 1531\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(42a-461\right){x}+1149a-1531$ |
| 108.6-c8 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{20} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( \frac{20281552375}{34012224} a + \frac{23002752625}{11337408} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a + 139\) , \( 269 a - 427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(2a+139\right){x}+269a-427$ |
| 108.6-c9 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{20} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( -\frac{20281552375}{34012224} a + \frac{44644905125}{17006112} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 146\) , \( -21 a - 397\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-3a-146\right){x}-21a-397$ |
| 108.6-c10 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{26} \cdot 3^{16} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( \frac{28681134125}{2985984} a + \frac{14290715375}{1492992} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -55 a + 228\) , \( 421 a + 757\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-55a+228\right){x}+421a+757$ |
| 108.6-c11 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{16} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( -\frac{28681134125}{2985984} a + \frac{19087521625}{995328} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -6 a + 58\) , \( -47 a - 35\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-6a+58\right){x}-47a-35$ |
| 108.6-c12 |
108.6-c |
$12$ |
$24$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
108.6 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{13} \) |
$1.38152$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.205685550$ |
2.011222529 |
\( -\frac{354186588125}{186624} a + \frac{187311714875}{186624} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4 a - 137\) , \( -17 a - 575\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(4a-137\right){x}-17a-575$ |
*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.
