| 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 |
| 81.1-CMa2 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{10} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.346779163 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) |
${y}^2+{y}={x}^{3}-30{x}+63$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$0.92865$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.900958696 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^{3}-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$1.22848$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.681060757 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^{3}-270{x}-1708$ |
| 729.4-b2 |
729.4-b |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$1.31330$ |
$(-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.349576835$ |
$0.900958696$ |
1.719560635 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^{3}-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$1.53999$ |
$(-a), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.571787496$ |
$0.900958696$ |
1.707899690 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^{3}-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$1.03826$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3Cs.1.1, 5Nn.1.1.1 |
$1$ |
\( 3 \) |
$0.135197028$ |
$2.702876088$ |
1.132214990 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.02394$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.413388200 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.07652$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$3.118107923$ |
$0.900958696$ |
2.512702187 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-c2 |
729.4-c |
$4$ |
$27$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.22682$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$3.391021540$ |
$0.900958696$ |
2.548188217 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$1.31330$ |
$(3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.251525634$ |
$2.702876088$ |
1.665267531 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-b2 |
729.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.58524$ |
$(3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.009274303$ |
$0.900958696$ |
3.895612925 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.74697$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$4.854482209$ |
$0.900958696$ |
2.957152791 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$1.67414$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.865613115 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a1 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$2.93664$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$0.900958696$ |
1.139632622 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.04477$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$0.900958696$ |
1.099159304 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-47}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.18324$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$4.692411943$ |
$0.900958696$ |
2.466675812 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$1.91445$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 17$ |
3Cs.1.1, 17Nn.3.7.1 |
$1$ |
\( 3 \) |
$0.471746728$ |
$2.702876088$ |
2.142551111 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.34828$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.249880982 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.44351$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.971881966 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-d2 |
729.4-d |
$4$ |
$27$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.47468$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$7.911362464$ |
$0.900958696$ |
3.809975138 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.56653$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$3.931045340$ |
$0.900958696$ |
1.844365202 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.80065$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.220139246 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.82891$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$9.700410033$ |
$0.900958696$ |
4.239362057 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$3.91246$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$6.200810795$ |
$0.900958696$ |
2.652065087 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.12700$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.202731545 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.23019$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$6.678624801$ |
$0.900958696$ |
2.641878694 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$2.45697$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.589815917 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$2.50046$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 29$ |
3Cs.1.1, 29Nn.1.2.1 |
$1$ |
\( 3 \) |
$0.733852072$ |
$2.702876088$ |
2.551856687 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-b2 |
729.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.35574$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.768340157 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.42936$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.188892267 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-b2 |
729.4-b |
$4$ |
$27$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.52566$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$11.51118954$ |
$0.900958696$ |
4.256212231 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a2 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-103}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.71237$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.177548196 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-b2 |
729.4-b |
$4$ |
$27$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.73519$ |
$(3,a+1), (3,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
|
\( 1 \) |
$1$ |
$0.900958696$ |
4.659185008 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-a2 |
729.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-107}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.80300$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$11.04022034$ |
$0.900958696$ |
3.846367046 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$2.82437$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.513091290 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-b2 |
729.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-115}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$4.97931$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.672118652 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.4-e2 |
729.4-e |
$4$ |
$27$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
729.4 |
\( 3^{6} \) |
\( 3^{22} \) |
$5.06517$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$8.664075157$ |
$1.801917392$ |
2.862289800 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$2.93664$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$2.702876088$ |
1.973901604 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-123}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$2.97312$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 41$ |
3Cs.1.1, 41Nn.3.11.1 |
$1$ |
\( 3 \) |
$0.924727711$ |
$2.702876088$ |
2.704386125 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$3.07997$ |
$(3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1.008762844$ |
$2.702876088$ |
2.847800056 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-159}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$3.38032$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 53$ |
3Cs.1.1, 53Nn.1.17.1 |
|
\( 3 \) |
$1$ |
$2.702876088$ |
3.365982008 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 729.1-a1 |
729.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{22} \) |
$5.92808$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.900958696$ |
0.141137062 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$3.47468$ |
$(3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1.739234555$ |
$2.702876088$ |
4.352220566 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-183}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$3.62648$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.399604699 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-219}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$3.96718$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.365286880 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-57}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$4.04788$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.358004683 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-231}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$4.07442$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1.540139751$ |
$2.702876088$ |
3.286711030 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-66}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$4.35574$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$4$ |
\( 1 \) |
$1$ |
$2.702876088$ |
1.330804190 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-267}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$4.38042$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 89$ |
3Cs.1.1, 89Nn.6.40.1 |
|
\( 3 \) |
$1$ |
$2.702876088$ |
3.047052003 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-b2 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{-69}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$4.45363$ |
$(3,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
|
\( 3 \) |
$1$ |
$2.702876088$ |
4.076958229 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
*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.
