| 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 |
| 21.1-a1 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{16} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$11.79695750$ |
$0.862076929$ |
1.850983143 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-306{x}+5859$ |
| 21.1-a2 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.474619687$ |
$6.896615437$ |
1.850983143 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+9{x}$ |
| 21.1-a3 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{20} \cdot 7^{4} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.949239375$ |
$3.448307718$ |
1.850983143 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-36{x}+27$ |
| 21.1-a4 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{28} \cdot 7^{2} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.474619687$ |
$1.724153859$ |
1.850983143 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-351{x}-2430$ |
| 21.1-a5 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$5.898478750$ |
$1.724153859$ |
1.850983143 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-441{x}+3672$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$11.79695750$ |
$0.862076929$ |
1.850983143 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-b1 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{28} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.862076929$ |
0.627613736 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1667\) , \( 72764\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1667{x}+72764$ |
| 21.1-b2 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{14} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$6.896615437$ |
0.627613736 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 48\) , \( 48\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+48{x}+48$ |
| 21.1-b3 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{16} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.448307718$ |
0.627613736 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -197\) , \( 146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-197{x}+146$ |
| 21.1-b4 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{14} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.724153859$ |
0.627613736 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1912\) , \( -32782\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1912{x}-32782$ |
| 21.1-b5 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{20} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.627613736 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2402\) , \( 44246\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2402{x}+44246$ |
| 21.1-b6 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.627613736 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -38417\) , \( 2882228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-38417{x}+2882228$ |
| 21.1-c1 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
2.824261813 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^3-34{x}-217$ |
| 21.1-c2 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$9$ |
\( 2^{3} \) |
$1$ |
$6.896615437$ |
2.824261813 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}$ |
| 21.1-c3 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2^{4} \) |
$1$ |
$3.448307718$ |
2.824261813 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^3-4{x}-1$ |
| 21.1-c4 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2^{5} \) |
$1$ |
$1.724153859$ |
2.824261813 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^3-39{x}+90$ |
| 21.1-c5 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2^{3} \) |
$1$ |
$1.724153859$ |
2.824261813 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^3-49{x}-136$ |
| 21.1-c6 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
2.824261813 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^3-784{x}-8515$ |
| 21.1-d1 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.638508823$ |
$0.862076929$ |
3.311928761 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -29 a + 4414\) , \( -25725 a - 68397\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-29a+4414\right){x}-25725a-68397$ |
| 21.1-d2 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$6.896615437$ |
3.311928761 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6 a + 179\) , \( -35 a + 210\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(6a+179\right){x}-35a+210$ |
| 21.1-d3 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.638508823$ |
$3.448307718$ |
3.311928761 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 784\) , \( -105 a - 5961\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(a+784\right){x}-105a-5961$ |
| 21.1-d4 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.319254411$ |
$1.724153859$ |
3.311928761 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -34 a + 5019\) , \( 11165 a - 37300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-34a+5019\right){x}+11165a-37300$ |
| 21.1-d5 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.277017646$ |
$1.724153859$ |
3.311928761 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44 a + 6229\) , \( -15855 a - 76746\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-44a+6229\right){x}-15855a-76746$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \cdot 11^{12} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$10.55403529$ |
$0.862076929$ |
3.311928761 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -779 a + 95164\) , \( -1013985 a - 1979955\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-779a+95164\right){x}-1013985a-1979955$ |
| 28.1-a1 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.790171969$ |
$0.875417135$ |
8.002117896 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -166 a + 20930\) , \( -103170 a - 313029\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-166a+20930\right){x}-103170a-313029$ |
| 28.1-a2 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$2.790171969$ |
$7.878754216$ |
8.002117896 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a + 360\) , \( 10 a - 1575\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(4a+360\right){x}+10a-1575$ |
| 28.1-a3 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.790171969$ |
$2.626251405$ |
8.002117896 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 9 a - 245\) , \( -760 a + 3749\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(9a-245\right){x}-760a+3749$ |
| 28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3 \) |
$2.790171969$ |
$1.313125702$ |
8.002117896 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -31 a + 4595\) , \( -8040 a - 52395\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-31a+4595\right){x}-8040a-52395$ |
| 28.1-a5 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$2.790171969$ |
$3.939377108$ |
8.002117896 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -6 a + 1570\) , \( 1550 a - 12223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-6a+1570\right){x}+1550a-12223$ |
| 28.1-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \cdot 11^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3^{2} \) |
$2.790171969$ |
$0.437708567$ |
8.002117896 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -2726 a + 330690\) , \( -6590210 a - 9977541\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-2726a+330690\right){x}-6590210a-9977541$ |
| 28.1-b1 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$0.815404895$ |
$0.875417135$ |
4.677106774 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 28.1-b2 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$7.338644063$ |
$7.878754216$ |
4.677106774 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 28.1-b3 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$2.446214687$ |
$2.626251405$ |
4.677106774 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 28.1-b4 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$4.892429375$ |
$1.313125702$ |
4.677106774 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 28.1-b5 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$14.67728812$ |
$3.939377108$ |
4.677106774 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 28.1-b6 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1.630809791$ |
$0.437708567$ |
4.677106774 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 28.1-c1 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{14} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
2.867965839 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -8355\) , \( 291341\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-8355{x}+291341$ |
| 28.1-c2 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{14} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.878754216$ |
2.867965839 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-25{x}-111$ |
| 28.1-c3 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{18} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
2.867965839 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+220{x}+2192$ |
| 28.1-c4 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{24} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$16$ |
\( 2 \cdot 3 \) |
$1$ |
$1.313125702$ |
2.867965839 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-1740{x}+22184$ |
| 28.1-c5 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{16} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$16$ |
\( 2 \) |
$1$ |
$3.939377108$ |
2.867965839 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-515{x}-4717$ |
| 28.1-c6 |
28.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{16} \) |
$4.51754$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$16$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
2.867965839 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-133795{x}+18781197$ |
| 28.1-d1 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$17.01778343$ |
$0.875417135$ |
10.84587145 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1535{x}+23591$ |
| 28.1-d2 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$1.890864825$ |
$7.878754216$ |
10.84587145 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-5{x}-7$ |
| 28.1-d3 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$5.672594476$ |
$2.626251405$ |
10.84587145 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+40{x}+155$ |
| 28.1-d4 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$11.34518895$ |
$1.313125702$ |
10.84587145 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-320{x}+1883$ |
| 28.1-d5 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$3.781729651$ |
$3.939377108$ |
10.84587145 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-95{x}-331$ |
| 28.1-d6 |
28.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$4.51754$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$34.03556686$ |
$0.437708567$ |
10.84587145 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-24575{x}+1488935$ |
| 49.1-a1 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$5.19590$ |
$(7,a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.6.2 |
$1$ |
\( 2 \) |
$7.084860660$ |
$4.944504600$ |
6.375885724 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -20\) , \( 46\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-20{x}+46$ |
| 49.1-a2 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \cdot 11^{12} \) |
$5.19590$ |
$(7,a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.6.2 |
$1$ |
\( 2 \) |
$7.084860660$ |
$4.944504600$ |
6.375885724 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -17 a + 542\) , \( -25 a - 3541\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-17a+542\right){x}-25a-3541$ |
*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.
