| 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 |
| 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 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 4\) , \( 4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-4a+4\right){x}+4$ |
| 648.1-a3 |
648.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{16} \) |
$0.90170$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.423564678$ |
1.211782339 |
\( \frac{35152}{9} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 9\) , \( -4 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+9{x}-4i$ |
| 5184.4-a3 |
5184.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5184.4 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.00611$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.637754311$ |
$1.211782339$ |
3.000435819 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^{3}-39{x}-70$ |
| 648.3-a3 |
648.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.27520$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.269818466$ |
$2.423564678$ |
1.849572148 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -8\) , \( 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-8{x}+14$ |
| 5184.3-k3 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.211782339$ |
2.922928979 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^{3}-39{x}-70$ |
| 192.4-b3 |
192.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
192.4 |
\( 2^{6} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$1.28828$ |
$(2,a), (2,a+1), (3,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
1.877285127 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 12\) , \( 12 a - 28\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(4a+12\right){x}+12a-28$ |
| 5184.1-a3 |
5184.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
5184.1 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.30508$ |
$(2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.211782339$ |
2.224015477 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.3-b3 |
648.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.01626$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.423564678$ |
2.167702147 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
1.484124205 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+2{x}+2$ |
| 192.4-e3 |
192.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
192.4 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{16} \) |
$2.07729$ |
$(2,a), (2,a+1), (3,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.862561557$ |
$3.635347017$ |
3.332716719 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.1-b3 |
648.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.85143$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.420832344$ |
$2.423564678$ |
4.355694791 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 5184.1-a3 |
5184.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
5184.1 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$4.97209$ |
$(2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.211782339$ |
1.478360594 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 192.1-b3 |
192.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \cdot 17^{12} \) |
$2.37547$ |
$(3,a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.540027220$ |
$3.635347017$ |
5.172007517 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1252\) , \( 12320\bigr] \) |
${y}^2={x}^3+{x}^2-1252{x}+12320$ |
| 648.1-a3 |
648.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.25113$ |
$(2,a+1), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.094658422$ |
$2.423564678$ |
6.849013235 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.3-e3 |
648.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.37385$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.573580810$ |
$2.423564678$ |
6.667889553 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 5184.1-a3 |
5184.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
5184.1 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$6.20643$ |
$(2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.211782339$ |
1.184342200 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.3-f3 |
648.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$3.71781$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.423564678$ |
1.175601548 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{12} \) |
$1.81272$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
1.586595513 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -3 a + 22\) , \( -a - 78\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-3a+22\right){x}-a-78$ |
| 192.4-b3 |
192.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
192.4 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{16} \) |
$3.10258$ |
$(2,a), (2,a+1), (3,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
0.779500221 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.1-a3 |
648.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$4.22935$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$2.290656370$ |
$2.423564678$ |
4.734381047 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 648.3-a3 |
648.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$4.59779$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1.157229302$ |
$2.423564678$ |
8.800499952 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 192.4-b3 |
192.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
192.4 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{16} \) |
$3.50449$ |
$(2,a), (2,a+1), (3,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$8.802095865$ |
$7.270694035$ |
6.074359257 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^3-39{x}-70$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 5^{12} \) |
$2.16662$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.124911523$ |
$7.270694035$ |
2.986507453 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 12\) , \( 102\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+12{x}+102$ |
| 24.1-c3 |
24.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{12} \) |
$2.27237$ |
$(2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$3.234548855$ |
$7.270694035$ |
4.093856489 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 5 a + 53\) , \( -22 a - 208\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(5a+53\right){x}-22a-208$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{12} \) |
$2.56357$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
2.243784892 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( 258\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-2{x}+258$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-57}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{12} \) |
$2.98647$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.963026950 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 13 a + 44\) , \( -111 a - 470\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(13a+44\right){x}-111a-470$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-66}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{12} \) |
$3.21361$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.832319552$ |
$7.270694035$ |
5.069628637 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 4\) , \( 1014\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+4{x}+1014$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-69}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{12} \) |
$3.28584$ |
$(2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$8.682821893$ |
$7.270694035$ |
7.599975922 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 15 a + 91\) , \( -188 a - 538\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(15a+91\right){x}-188a-538$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-78}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{12} \) |
$3.49356$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
1.646487975 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -30\) , \( 1626\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-30{x}+1626$ |
| 24.1-c3 |
24.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-93}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{12} \) |
$3.81472$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.753935850 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 23 a + 42\) , \( -375 a - 366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(23a+42\right){x}-375a-366$ |
| 24.1-a3 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-102}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{12} \) |
$3.99504$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$3.525927436$ |
$7.270694035$ |
5.076672517 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -28\) , \( 3694\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-28{x}+3694$ |
| 24.1-g3 |
24.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 19^{12} \) |
$4.05337$ |
$(2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.312474026$ |
$7.270694035$ |
6.563236808 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 25 a + 105\) , \( -506 a - 44\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(25a+105\right){x}-506a-44$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-114}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 19^{12} \) |
$4.22351$ |
$(2,a), (3,a)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
5.447703099 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -82\) , \( 5066\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-82{x}+5066$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 23^{12} \) |
$4.49279$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$14.54138807$ |
0.640148915 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 33 a + 16\) , \( -791 a + 1194\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(33a+16\right){x}-791a+1194$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-138}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 23^{12} \) |
$4.64687$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.678512251$ |
$14.54138807$ |
3.315583416 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -84\) , \( 9102\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-84{x}+9102$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-141}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 37^{12} \) |
$4.69711$ |
$(2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$14.54138807$ |
10.93180382 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 29 a + 1639\) , \( 1003 a - 31690\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(29a+1639\right){x}+1003a-31690$ |
| 24.1-c3 |
24.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 29^{12} \) |
$5.08117$ |
$(2,a+1), (3,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$4.598000648$ |
$14.54138807$ |
10.41029212 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 43 a - 34\) , \( -1359 a + 5170\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(43a-34\right){x}-1359a+5170$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-174}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 29^{12} \) |
$5.21790$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$6.456802054$ |
$14.54138807$ |
7.117848059 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -164\) , \( 18198\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-164{x}+18198$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-177}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 31^{12} \) |
$5.26269$ |
$(2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$14.54138807$ |
8.802752309 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 45 a + 61\) , \( -1598 a + 7256\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(45a+61\right){x}-1598a+7256$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-186}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 31^{12} \) |
$5.39483$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$14.54138807$ |
1.066226304 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -258\) , \( 22002\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-258{x}+22002$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-201}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 47^{12} \) |
$5.60815$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$36$ |
\( 2^{2} \) |
$1$ |
$14.54138807$ |
4.615516946 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 81 a + 2176\) , \( -393 a - 72474\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(81a+2176\right){x}-393a-72474$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 41^{12} \) |
$5.73233$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1.858614181$ |
$14.54138807$ |
7.460113850 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 90 a + 883\) , \( -3022 a - 28980\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a-1\right){x}^2+\left(90a+883\right){x}-3022a-28980$ |
| 24.1-c3 |
24.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-213}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 37^{12} \) |
$5.77313$ |
$(2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$14.54138807$ |
9.382402665 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 55 a + 3\) , \( -2372 a + 15982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(55a+3\right){x}-2372a+15982$ |
| 24.1-c3 |
24.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-222}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 37^{12} \) |
$5.89383$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$14.54138807$ |
0.975954065 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -382\) , \( 37418\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-382{x}+37418$ |
| 24.1-a3 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-237}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 41^{12} \) |
$6.08969$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$14.54138807$ |
0.472282328 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 63 a - 206\) , \( -2951 a + 24210\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(63a-206\right){x}-2951a+24210$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-246}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 41^{12} \) |
$6.20424$ |
$(2,a), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$14.54138807$ |
7.234910114 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -396\) , \( 51294\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-396{x}+51294$ |
| 24.1-d3 |
24.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-249}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \cdot 43^{12} \) |
$6.24196$ |
$(2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$14.54138807$ |
11.75797750 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 65 a - 79\) , \( -3298 a + 29372\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(65a-79\right){x}-3298a+29372$ |
| 648.1-a4 |
648.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.27520$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.578011356$ |
1.339615804 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -10\) , \( -14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-10{x}-14$ |
| 24.1-b4 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
0.820343793 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 3 a - 9\) , \( 7 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(3a-9\right){x}+7a-14$ |
| 192.1-e3 |
192.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.52431$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$11.36701703$ |
2.480486475 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 59\) , \( 75 a - 210\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(22a-59\right){x}+75a-210$ |
*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.
