| 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 |
| 75.1-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{44} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.497953220$ |
$0.558925428$ |
7.002156534 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$ |
| 75.1-a2 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.497953220$ |
$8.942806850$ |
7.002156534 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5$ |
| 75.1-a3 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{16} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.248976610$ |
$1.117850856$ |
7.002156534 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+315{x}+1066$ |
| 75.1-a4 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{8} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1.124488305$ |
$2.235701712$ |
7.002156534 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 75.1-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.248976610$ |
$4.471403425$ |
7.002156534 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-45{x}-104$ |
| 75.1-a6 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{28} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$2.248976610$ |
$1.117850856$ |
7.002156534 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$ |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$4.497953220$ |
$2.235701712$ |
7.002156534 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$ |
| 75.1-a8 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$4.497953220$ |
$0.558925428$ |
7.002156534 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-19440{x}+1048135$ |
| 75.1-b1 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{44} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$34.66267784$ |
$0.558925428$ |
6.745109504 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -951\) , \( -19807\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-951{x}-19807$ |
| 75.1-b2 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.166417365$ |
$8.942806850$ |
6.745109504 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 39\) , \( -7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+39{x}-7$ |
| 75.1-b3 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{16} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.166417365$ |
$1.117850856$ |
6.745109504 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 354\) , \( -2023\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+354{x}-2023$ |
| 75.1-b4 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{8} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.166417365$ |
$2.235701712$ |
6.745109504 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -51\) , \( 83\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-51{x}+83$ |
| 75.1-b5 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.166417365$ |
$4.471403425$ |
6.745109504 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( 227\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-6{x}+227$ |
| 75.1-b6 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{28} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$8.665669460$ |
$1.117850856$ |
6.745109504 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1176\) , \( -12967\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-1176{x}-12967$ |
| 75.1-b7 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.166417365$ |
$2.235701712$ |
6.745109504 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -681\) , \( 9407\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-681{x}+9407$ |
| 75.1-b8 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$8.665669460$ |
$0.558925428$ |
6.745109504 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -19401\) , \( -989827\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-19401{x}-989827$ |
| 75.1-c1 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.778371427 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 75.1-c2 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$8.942806850$ |
0.778371427 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 75.1-c3 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.778371427 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 75.1-c4 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
0.778371427 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 75.1-c5 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
0.778371427 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 75.1-c6 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.778371427 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 75.1-c7 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.778371427 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 75.1-c8 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.778371427 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 75.1-d1 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$9.352879577$ |
$0.558925428$ |
3.640007112 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -76\) , \( 1094\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-76{x}+1094$ |
| 75.1-d2 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.338219894$ |
$8.942806850$ |
3.640007112 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 34\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+34{x}-6$ |
| 75.1-d3 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.676439788$ |
$1.117850856$ |
3.640007112 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 69\) , \( -48\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+69{x}-48$ |
| 75.1-d4 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$2.338219894$ |
$2.235701712$ |
3.640007112 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 24\) , \( 24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+24{x}+24$ |
| 75.1-d5 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.169109947$ |
$4.471403425$ |
3.640007112 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 29\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+29{x}+2$ |
| 75.1-d6 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$4.676439788$ |
$1.117850856$ |
3.640007112 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -101\) , \( 924\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-101{x}+924$ |
| 75.1-d7 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$0.584554973$ |
$2.235701712$ |
3.640007112 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -46\) , \( -88\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-46{x}-88$ |
| 75.1-d8 |
75.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$3.02128$ |
$(3,a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$9.352879577$ |
$0.558925428$ |
3.640007112 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2126\) , \( 43854\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-2126{x}+43854$ |
*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.
