| 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 |
| 15.1-a1 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.408181419 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$8.942806850$ |
0.408181419 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
0.408181419 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
0.408181419 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
0.408181419 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
0.408181419 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
0.408181419 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.408181419 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.558925428$ |
1.632725679 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -411\) , \( -5721\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-411{x}-5721$ |
| 15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$8.942806850$ |
1.632725679 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 29\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+29{x}-1$ |
| 15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
1.632725679 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 169\) , \( -645\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+169{x}-645$ |
| 15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
1.632725679 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -11\) , \( 39\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-11{x}+39$ |
| 15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
1.632725679 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 9\) , \( 75\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+9{x}+75$ |
| 15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
1.632725679 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -511\) , \( -3661\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-511{x}-3661$ |
| 15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
1.632725679 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -291\) , \( 2895\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-291{x}+2895$ |
| 15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.558925428$ |
1.632725679 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -8611\) , \( -290401\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-8611{x}-290401$ |
| 15.1-c1 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{44} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$14.85962321$ |
$0.558925428$ |
3.032711051 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$ |
| 15.1-c2 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.928726450$ |
$8.942806850$ |
3.032711051 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5$ |
| 15.1-c3 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.857452901$ |
$1.117850856$ |
3.032711051 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+315{x}+1066$ |
| 15.1-c4 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{8} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$3.714905803$ |
$2.235701712$ |
3.032711051 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 15.1-c5 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.857452901$ |
$4.471403425$ |
3.032711051 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-45{x}-104$ |
| 15.1-c6 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{28} \cdot 5^{4} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$7.429811606$ |
$1.117850856$ |
3.032711051 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$ |
| 15.1-c7 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$0.928726450$ |
$2.235701712$ |
3.032711051 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$ |
| 15.1-c8 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{2} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$14.85962321$ |
$0.558925428$ |
3.032711051 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-19440{x}+1048135$ |
| 15.1-d1 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{14} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$5.298196352$ |
$0.558925428$ |
4.325250620 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2751{x}-104477$ |
| 15.1-d2 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.324549088$ |
$8.942806850$ |
4.325250620 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}+23$ |
| 15.1-d3 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{28} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.662274544$ |
$1.117850856$ |
4.325250620 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+874{x}-5227$ |
| 15.1-d4 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{20} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.324549088$ |
$2.235701712$ |
4.325250620 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-251{x}-727$ |
| 15.1-d5 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.649098176$ |
$4.471403425$ |
4.325250620 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-126{x}+523$ |
| 15.1-d6 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.649098176$ |
$1.117850856$ |
4.325250620 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-3376{x}-75727$ |
| 15.1-d7 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$5.298196352$ |
$2.235701712$ |
4.325250620 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2001{x}+34273$ |
| 15.1-d8 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{14} \) |
$1.92642$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$5.298196352$ |
$0.558925428$ |
4.325250620 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-54001{x}-4834477$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
0.781794306 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
0.781794306 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
0.781794306 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
0.781794306 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{24} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$3.371581646$ |
$2.141031885$ |
2.635883335 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -213\) , \( -1517\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-213{x}-1517$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{16} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.123860548$ |
$6.423095656$ |
2.635883335 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 37\) , \( -17\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+37{x}-17$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \) |
$0.561930274$ |
$6.423095656$ |
2.635883335 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \) |
${y}^2={x}^3-12{x}-11$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{6} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1.685790823$ |
$2.141031885$ |
2.635883335 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -372\) , \( 2761\bigr] \) |
${y}^2={x}^3-372{x}+2761$ |
| 20.1-c1 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{12} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$2.141031885$ |
2.345382920 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -48\) , \( 628\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-48{x}+628$ |
| 20.1-c2 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$6.423095656$ |
2.345382920 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 42\) , \( -38\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+42{x}-38$ |
| 20.1-c3 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{14} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$6.423095656$ |
2.345382920 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 62\bigr] \) |
${y}^2={x}^3-{x}^2-33{x}+62$ |
| 20.1-c4 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{18} \) |
$2.07008$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$2.141031885$ |
2.345382920 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) |
${y}^2={x}^3-{x}^2-1033{x}-12438$ |
| 20.1-d1 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.957327600$ |
$2.141031885$ |
4.590682724 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 15\) , \( -13\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+15{x}-13$ |
| 20.1-d2 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.652442533$ |
$6.423095656$ |
4.590682724 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 25\) , \( -25\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+25{x}-25$ |
| 20.1-d3 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$0.326221266$ |
$6.423095656$ |
4.590682724 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 5\bigr] \) |
${y}^2={x}^3-{x}^2-5{x}+5$ |
| 20.1-d4 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{6} \) |
$2.07008$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$0.978663800$ |
$2.141031885$ |
4.590682724 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -165\) , \( -763\bigr] \) |
${y}^2={x}^3-{x}^2-165{x}-763$ |
| 24.1-a1 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$2.16662$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
1.327441044 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 24.1-a2 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.16662$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
1.327441044 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
*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.
