| 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 |
| 2592.3-a1 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.240339345$ |
$0.781788099$ |
2.742676397 |
\( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -45 a + 199\) , \( 747 a + 424\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-45a+199\right){x}+747a+424$ |
| 2592.3-a2 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.240339345$ |
$0.781788099$ |
2.742676397 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 45 a + 199\) , \( -747 a + 424\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(45a+199\right){x}-747a+424$ |
| 2592.3-a3 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.620169672$ |
$1.563576199$ |
2.742676397 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 19\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+19{x}+10$ |
| 2592.3-a4 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.310084836$ |
$1.563576199$ |
2.742676397 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( -20\bigr] \) |
${y}^2={x}^{3}-21{x}-20$ |
| 2592.3-a5 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.620169672$ |
$1.563576199$ |
2.742676397 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -92\bigr] \) |
${y}^2={x}^{3}-39{x}-92$ |
| 2592.3-a6 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{14} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.620169672$ |
$1.563576199$ |
2.742676397 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -72\) , \( 275\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-72{x}+275$ |
| 2592.3-b1 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 720 a - 288\) , \( 8374 a + 4948\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(720a-288\right){x}+8374a+4948$ |
| 2592.3-b2 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -720 a - 287\) , \( 9094 a - 4659\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-720a-287\right){x}+9094a-4659$ |
| 2592.3-b3 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -68 a\bigr] \) |
${y}^2={x}^{3}+15{x}-68a$ |
| 2592.3-b4 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{29} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -90 a - 107\) , \( -356 a - 339\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-90a-107\right){x}-356a-339$ |
| 2592.3-b5 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{29} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 90 a - 108\) , \( -446 a + 448\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(90a-108\right){x}-446a+448$ |
| 2592.3-b6 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a - 18\) , \( 112 a + 88\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(45a-18\right){x}+112a+88$ |
| 2592.3-b7 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -45 a - 17\) , \( 157 a - 69\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-45a-17\right){x}+157a-69$ |
| 2592.3-b8 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 105\) , \( 292 a\bigr] \) |
${y}^2={x}^{3}+105{x}+292a$ |
| 2592.3-c1 |
2592.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.250591196$ |
$3.969390382$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 2592.3-c2 |
2592.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.125295598$ |
$3.969390382$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 2592.3-d1 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.444312937$ |
$2.291728606$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+9{x}$ |
| 2592.3-d2 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.222156468$ |
$2.291728606$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) |
${y}^2={x}^{3}-9{x}$ |
| 2592.3-d3 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.444312937$ |
$2.291728606$ |
2.880030840 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -24\) , \( -35\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-24{x}-35$ |
| 2592.3-d4 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.444312937$ |
$2.291728606$ |
2.880030840 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -23\) , \( 60\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-23{x}+60$ |
| 2592.3-e1 |
2592.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \) |
${y}^2={x}^{3}-27{x}$ |
| 2592.3-e2 |
2592.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 2592.3-f1 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 720 a - 287\) , \( -9094 a - 4659\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(720a-287\right){x}-9094a-4659$ |
| 2592.3-f2 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -720 a - 288\) , \( -8374 a + 4948\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-720a-288\right){x}-8374a+4948$ |
| 2592.3-f3 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 68 a\bigr] \) |
${y}^2={x}^{3}+15{x}+68a$ |
| 2592.3-f4 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{29} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -90 a - 108\) , \( 446 a + 448\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-90a-108\right){x}+446a+448$ |
| 2592.3-f5 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{29} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 90 a - 107\) , \( 356 a - 339\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(90a-107\right){x}+356a-339$ |
| 2592.3-f6 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 45 a - 17\) , \( -157 a - 69\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(45a-17\right){x}-157a-69$ |
| 2592.3-f7 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -45 a - 18\) , \( -112 a + 88\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-45a-18\right){x}-112a+88$ |
| 2592.3-f8 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.117830943$ |
1.580851681 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 105\) , \( -292 a\bigr] \) |
${y}^2={x}^{3}+105{x}-292a$ |
| 2592.3-g1 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.781788099$ |
2.211230666 |
\( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -45 a + 198\) , \( -702 a - 621\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-45a+198\right){x}-702a-621$ |
| 2592.3-g2 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.781788099$ |
2.211230666 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a + 198\) , \( 702 a - 621\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(45a+198\right){x}+702a-621$ |
| 2592.3-g3 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.563576199$ |
2.211230666 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( -27\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}-27$ |
| 2592.3-g4 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.563576199$ |
2.211230666 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \) |
${y}^2={x}^{3}-21{x}+20$ |
| 2592.3-g5 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.563576199$ |
2.211230666 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( 92\bigr] \) |
${y}^2={x}^{3}-39{x}+92$ |
| 2592.3-g6 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{14} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.563576199$ |
2.211230666 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -71\) , \( -202\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-71{x}-202$ |
*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.
