| 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 |
| 4761.2-a1 |
4761.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$0.271601507$ |
4.233848486 |
\( -\frac{5992448}{729} a - \frac{10338304}{729} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -245 a - 147\) , \( 1268 a - 7295\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-245a-147\right){x}+1268a-7295$ |
| 4761.2-b1 |
4761.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{2} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.262431948$ |
2.460916233 |
\( -\frac{5992448}{729} a - \frac{10338304}{729} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -45 a - 75\) , \( 195 a + 330\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-45a-75\right){x}+195a+330$ |
| 4761.2-c1 |
4761.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{10} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.025878195$ |
2.605546602 |
\( -\frac{41656}{9} a + \frac{21737}{9} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 22 a - 42\) , \( 94 a - 163\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(22a-42\right){x}+94a-163$ |
| 4761.2-c2 |
4761.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{14} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.512939097$ |
2.605546602 |
\( \frac{932449124}{81} a + \frac{1615060753}{81} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -38 a + 33\) , \( 355 a - 541\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-38a+33\right){x}+355a-541$ |
| 4761.2-d1 |
4761.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{10} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.675670186$ |
0.195049182 |
\( -\frac{41656}{9} a + \frac{21737}{9} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -369 a - 696\) , \( -6290 a - 11009\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-369a-696\right){x}-6290a-11009$ |
| 4761.2-d2 |
4761.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{14} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.337835093$ |
0.195049182 |
\( \frac{932449124}{81} a + \frac{1615060753}{81} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -6429 a - 11061\) , \( -369269 a - 640430\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6429a-11061\right){x}-369269a-640430$ |
| 4761.2-e1 |
4761.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{10} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.158530836$ |
1.246228359 |
\( \frac{139573}{9} a - \frac{75116}{3} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -1580 a - 2769\) , \( 8982 a + 15644\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1580a-2769\right){x}+8982a+15644$ |
| 4761.2-f1 |
4761.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{6} \cdot 23^{7} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.728827018$ |
0.998138744 |
\( -\frac{80756}{23} a - \frac{25367}{23} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -52 a - 98\) , \( -334 a - 581\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-52a-98\right){x}-334a-581$ |
| 4761.2-f2 |
4761.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.728827018$ |
0.998138744 |
\( \frac{9537774883}{529} a + \frac{16527155318}{529} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -877 a - 1568\) , \( -19390 a - 33410\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-877a-1568\right){x}-19390a-33410$ |
| 4761.2-g1 |
4761.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{4} \) |
$2.57131$ |
$(a), (3a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.025185393$ |
$9.740235603$ |
3.399138213 |
\( \frac{139573}{9} a - \frac{75116}{3} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 11 a - 26\) , \( -30 a + 54\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-26\right){x}-30a+54$ |
| 4761.2-h1 |
4761.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.605301715$ |
$2.412710497$ |
4.472303333 |
\( 13377 a + 24696 \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -29 a + 6\) , \( -7 a - 112\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-29a+6\right){x}-7a-112$ |
| 4761.2-i1 |
4761.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{2} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.199141493$ |
$19.81607472$ |
4.556682399 |
\( 13377 a + 24696 \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -3 a - 5\) , \( 7 a + 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-5\right){x}+7a+12$ |
| 4761.2-j1 |
4761.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.689604920$ |
$2.713221861$ |
2.160503764 |
\( -\frac{1688064}{529} a + \frac{2363328}{529} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 106 a - 188\) , \( -758 a + 1308\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(106a-188\right){x}-758a+1308$ |
| 4761.2-j2 |
4761.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{3} \cdot 23^{7} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.379209840$ |
$2.713221861$ |
2.160503764 |
\( \frac{19029504}{23} a + \frac{33109056}{23} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 1363 a - 2363\) , \( 30502 a - 52832\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(1363a-2363\right){x}+30502a-52832$ |
| 4761.2-k1 |
4761.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.507189525$ |
$11.01796852$ |
3.226347751 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 232 a - 402\) , \( -201 a + 348\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(232a-402\right){x}-201a+348$ |
| 4761.2-k2 |
4761.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.014379050$ |
$5.508984263$ |
3.226347751 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -17 a + 31\) , \( 15 a - 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17a+31\right){x}+15a-25$ |
| 4761.2-l1 |
4761.2-l |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{4} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$3.292361242$ |
1.900845649 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -3 a - 8\bigr] \) |
${y}^2+{y}={x}^{3}-3a-8$ |
| 4761.2-l2 |
4761.2-l |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{4} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.877083726$ |
1.900845649 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 3 a + 7\bigr] \) |
${y}^2+a{y}={x}^{3}+3a+7$ |
| 4761.2-m1 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.497831635$ |
$2.053969277$ |
3.552436393 |
\( -44330496 a + 76771008 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3691 a - 6399\) , \( 157587 a - 272948\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3691a-6399\right){x}+157587a-272948$ |
| 4761.2-m2 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.497831635$ |
$2.053969277$ |
3.552436393 |
\( -44330496 a + 76771008 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3691 a - 6399\) , \( -163986 a + 284021\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3691a-6399\right){x}-163986a+284021$ |
| 4761.2-m3 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.998554423$ |
$6.161907831$ |
3.552436393 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a + 7\) , \( 3 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+7\right){x}+3a-10$ |
| 4761.2-m4 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2^{3} \) |
$0.499277211$ |
$6.161907831$ |
3.552436393 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 66 a - 114\) , \( -57 a + 99\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(66a-114\right){x}-57a+99$ |
| 4761.2-m5 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.995663271$ |
$2.053969277$ |
3.552436393 |
\( 44330496 a + 76771008 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -32 a - 278\) , \( -1221 a - 527\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a-278\right){x}-1221a-527$ |
| 4761.2-m6 |
4761.2-m |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{6} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.995663271$ |
$2.053969277$ |
3.552436393 |
\( 44330496 a + 76771008 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -32 a - 278\) , \( 942 a + 432\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a-278\right){x}+942a+432$ |
| 4761.2-n1 |
4761.2-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{10} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.189061150$ |
0.686504775 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -1278 a + 2120\bigr] \) |
${y}^2+a{y}={x}^{3}-1278a+2120$ |
| 4761.2-n2 |
4761.2-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{10} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.189061150$ |
0.686504775 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1278 a - 2121\bigr] \) |
${y}^2+{y}={x}^{3}+1278a-2121$ |
| 4761.2-o1 |
4761.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.475174008$ |
$2.297405251$ |
3.283089468 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 160 a - 312\) , \( -156 a + 240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(160a-312\right){x}-156a+240$ |
| 4761.2-o2 |
4761.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$4.950348016$ |
$1.148702625$ |
3.283089468 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2375 a + 4117\) , \( 2058 a - 3562\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2375a+4117\right){x}+2058a-3562$ |
| 4761.2-p1 |
4761.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.489142567$ |
$4.419099858$ |
7.598702858 |
\( -\frac{1688064}{529} a + \frac{2363328}{529} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 106 a - 189\) , \( 758 a - 1309\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a-189\right){x}+758a-1309$ |
| 4761.2-p2 |
4761.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{3} \cdot 23^{7} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.744571283$ |
$8.838199717$ |
7.598702858 |
\( \frac{19029504}{23} a + \frac{33109056}{23} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1363 a - 2364\) , \( -30502 a + 52831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1363a-2364\right){x}-30502a+52831$ |
| 4761.2-q1 |
4761.2-q |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.164413030$ |
$4.532676057$ |
2.581555927 |
\( 13377 a + 24696 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -29 a + 6\) , \( 7 a + 111\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-29a+6\right){x}+7a+111$ |
| 4761.2-r1 |
4761.2-r |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{3} \cdot 23^{2} \) |
$2.57131$ |
$(a), (3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.178310053$ |
$12.69317010$ |
2.613456642 |
\( 13377 a + 24696 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -3 a - 6\) , \( -7 a - 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-3a-6\right){x}-7a-13$ |
| 4761.2-s1 |
4761.2-s |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{10} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$4$ |
\( 2^{2} \) |
$1$ |
$0.586917209$ |
2.710854471 |
\( \frac{139573}{9} a - \frac{75116}{3} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -1580 a - 2769\) , \( -8982 a - 15645\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1580a-2769\right){x}-8982a-15645$ |
| 4761.2-t1 |
4761.2-t |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{6} \cdot 23^{7} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.555480421$ |
1.892404193 |
\( -\frac{80756}{23} a - \frac{25367}{23} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -52 a - 99\) , \( 333 a + 579\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-52a-99\right){x}+333a+579$ |
| 4761.2-t2 |
4761.2-t |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{6} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.277740210$ |
1.892404193 |
\( \frac{9537774883}{529} a + \frac{16527155318}{529} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -877 a - 1569\) , \( 19389 a + 33408\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-877a-1569\right){x}+19389a+33408$ |
| 4761.2-u1 |
4761.2-u |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{9} \cdot 23^{4} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.991530778$ |
1.727161100 |
\( \frac{139573}{9} a - \frac{75116}{3} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 11 a - 27\) , \( 29 a - 56\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(11a-27\right){x}+29a-56$ |
| 4761.2-v1 |
4761.2-v |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{10} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.732560874$ |
1.366172647 |
\( -\frac{41656}{9} a + \frac{21737}{9} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 22 a - 41\) , \( -95 a + 161\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a-41\right){x}-95a+161$ |
| 4761.2-v2 |
4761.2-v |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{14} \cdot 23^{3} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.366280437$ |
1.366172647 |
\( \frac{932449124}{81} a + \frac{1615060753}{81} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -38 a + 34\) , \( -356 a + 539\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+34\right){x}-356a+539$ |
| 4761.2-w1 |
4761.2-w |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{10} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.748673053$ |
0.793473563 |
\( -\frac{41656}{9} a + \frac{21737}{9} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -369 a - 696\) , \( 6290 a + 11008\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-369a-696\right){x}+6290a+11008$ |
| 4761.2-w2 |
4761.2-w |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( - 3^{14} \cdot 23^{9} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.374336526$ |
0.793473563 |
\( \frac{932449124}{81} a + \frac{1615060753}{81} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -6429 a - 11061\) , \( 369269 a + 640429\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6429a-11061\right){x}+369269a+640429$ |
| 4761.2-x1 |
4761.2-x |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{8} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.359518334$ |
0.784918276 |
\( -\frac{5992448}{729} a - \frac{10338304}{729} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -245 a - 147\) , \( -1268 a + 7294\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-245a-147\right){x}-1268a+7294$ |
| 4761.2-y1 |
4761.2-y |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{18} \cdot 23^{2} \) |
$2.57131$ |
$(a), (3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.992450872$ |
1.150342047 |
\( -\frac{5992448}{729} a - \frac{10338304}{729} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -45 a - 75\) , \( -195 a - 331\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-45a-75\right){x}-195a-331$ |
*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.
