| 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 |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.51333$ |
$(11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.427595683 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$0.51333$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.851543623$ |
0.427595683 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.51333$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.257718117$ |
0.427595683 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 124.1-a1 |
124.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{50} \cdot 31 \) |
$0.51648$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.368431786$ |
0.425428381 |
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 1300 a - 550\) , \( -9800 a - 7280\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1300a-550\right){x}-9800a-7280$ |
| 124.1-a2 |
124.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31 \) |
$0.51648$ |
$(-6a+1), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.210794651$ |
0.425428381 |
\( -\frac{24551}{62} a + \frac{45753}{31} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}$ |
| 124.1-a3 |
124.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{10} \cdot 31^{5} \) |
$0.51648$ |
$(-6a+1), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.842158930$ |
0.425428381 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -15 a + 5\) , \( -7 a + 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-15a+5\right){x}-7a+21$ |
| 124.2-a1 |
124.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.2 |
\( 2^{2} \cdot 31 \) |
\( 2^{50} \cdot 31 \) |
$0.51648$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.368431786$ |
0.425428381 |
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -1301 a + 751\) , \( 10550 a - 16530\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1301a+751\right){x}+10550a-16530$ |
| 124.2-a2 |
124.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.2 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31 \) |
$0.51648$ |
$(6a-5), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.210794651$ |
0.425428381 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}$ |
| 124.2-a3 |
124.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.2 |
\( 2^{2} \cdot 31 \) |
\( 2^{10} \cdot 31^{5} \) |
$0.51648$ |
$(6a-5), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.842158930$ |
0.425428381 |
\( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 14 a - 9\) , \( -3 a + 9\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-9\right){x}-3a+9$ |
| 144.1-CMa1 |
144.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$0.53615$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.108115717$ |
0.491528664 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^{3}+1$ |
| 144.1-CMa2 |
144.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$0.53615$ |
$(-2a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.554057858$ |
0.491528664 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \) |
${y}^2={x}^{3}-15{x}+22$ |
| 147.2-a1 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{20} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.431038464$ |
0.497720347 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-470a+321\right){x}+1866a-3772$ |
| 147.2-a2 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{20} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.431038464$ |
0.497720347 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 470 a - 149\) , \( -1866 a - 1906\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(470a-149\right){x}-1866a-1906$ |
| 147.2-a3 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 147.2-a4 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.896615437$ |
0.497720347 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 147.2-a5 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.448307718$ |
0.497720347 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 147.2-a6 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.497720347 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 147.2-a7 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.497720347 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 147.2-a8 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 171.1-a1 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{3} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.713137527$ |
0.522143560 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-5\right){x}+9a+3$ |
| 171.1-a2 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{6} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.356568763$ |
0.522143560 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 25\) , \( 18 a + 48\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-20a+25\right){x}+18a+48$ |
| 171.1-a3 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$8.139412583$ |
0.522143560 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-a$ |
| 171.1-a4 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19^{2} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.069706291$ |
0.522143560 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5 a + 5\) , \( -11 a + 11\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a+5\right){x}-11a+11$ |
| 171.2-a1 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{3} \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.713137527$ |
0.522143560 |
\( -\frac{29840721}{6859} a - \frac{5426511}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 9\) , \( -10 a + 13\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-9\right){x}-10a+13$ |
| 171.2-a2 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{6} \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.356568763$ |
0.522143560 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 19 a + 6\) , \( -19 a + 67\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(19a+6\right){x}-19a+67$ |
| 171.2-a3 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$8.139412583$ |
0.522143560 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+1\right){x}$ |
| 171.2-a4 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{3} \cdot 19^{2} \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.069706291$ |
0.522143560 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -6 a + 11\) , \( 10 a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-6a+11\right){x}+10a+1$ |
| 192.1-a1 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.524717144 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 6\) , \( 11 a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(11a-6\right){x}+11a-1$ |
| 192.1-a2 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.524717144 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 11\) , \( -11 a + 10\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-11\right){x}-11a+10$ |
| 192.1-a3 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.908836754$ |
0.524717144 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(16a-16\right){x}-180$ |
| 192.1-a4 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.524717144 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(a-1\right){x}$ |
| 192.1-a5 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
0.524717144 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 4\) , \( 4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-4a+4\right){x}+4$ |
| 192.1-a6 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.524717144 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 24\) , \( -36\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-24a+24\right){x}-36$ |
| 192.1-a7 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.524717144 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 220\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-64a+64\right){x}+220$ |
| 192.1-a8 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.908836754$ |
0.524717144 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -384 a + 384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-384a+384\right){x}-2772$ |
| 196.2-a1 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
0.505422318 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.2-a2 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.505422318 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-a{x}$ |
| 196.2-a3 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
0.505422318 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a-5\right){x}-6$ |
| 196.2-a4 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.313125702$ |
0.505422318 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -36 a + 35\) , \( -70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-36a+35\right){x}-70$ |
| 196.2-a5 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{20} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
0.505422318 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 184 a - 415\) , \( 1880 a - 2686\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(184a-415\right){x}+1880a-2686$ |
| 196.2-a6 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{20} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
0.505422318 |
\( \frac{14378731676028886375}{3256827195820898} a + \frac{9866935598003002000}{1628413597910449} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 414 a - 185\) , \( -1880 a - 806\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(414a-185\right){x}-1880a-806$ |
| 196.2-a7 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.505422318 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -11 a + 10\) , \( 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-11a+10\right){x}+12$ |
| 196.2-a8 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{10} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
0.505422318 |
\( -\frac{10722436976428375}{161414428} a + \frac{3017980745593000}{40353607} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 184 a - 405\) , \( 1920 a - 2854\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(184a-405\right){x}+1920a-2854$ |
| 196.2-a9 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{10} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
0.505422318 |
\( \frac{10722436976428375}{161414428} a + \frac{1349486005943625}{161414428} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 404 a - 185\) , \( -1920 a - 934\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(404a-185\right){x}-1920a-934$ |
| 196.2-a10 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
0.505422318 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 228.1-a1 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{2} \cdot 19^{10} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.548223191$ |
0.633033614 |
\( -\frac{612993539767699445}{588582360748896} a + \frac{16582918214994847}{73572795093612} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 142 a - 105\) , \( 756 a + 161\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(142a-105\right){x}+756a+161$ |
| 228.1-a2 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{4} \cdot 3^{5} \cdot 19 \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.482231917$ |
0.633033614 |
\( \frac{212831}{2052} a + \frac{51428}{513} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+2a{x}$ |
| 228.1-a3 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3 \cdot 19^{5} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.096446383$ |
0.633033614 |
\( \frac{38854777864121}{7606576128} a - \frac{17432772730153}{7606576128} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -18 a + 55\) , \( 148 a + 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a+55\right){x}+148a+1$ |
| 228.1-a4 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{10} \cdot 19^{2} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.741115958$ |
0.633033614 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -8 a\) , \( -18 a + 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-8a{x}-18a+8$ |
| 228.2-a1 |
228.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.2 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{2} \cdot 19^{10} \) |
$0.60143$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.548223191$ |
0.633033614 |
\( \frac{612993539767699445}{588582360748896} a - \frac{160110064682580223}{196194120249632} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -140 a + 35\) , \( -615 a + 881\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-140a+35\right){x}-615a+881$ |
*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.
