| 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 |
| 576.1-a1 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$5.622957086$ |
1.874319028 |
\( \frac{1917985210250720370250}{3} a^{3} + \frac{3705262898043279737500}{3} a^{2} - \frac{513922588181516731250}{3} a - \frac{992822201275698608000}{3} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a + 1\) , \( a^{3} - 3 a\) , \( -237 a^{3} + 114 a^{2} + 898 a - 459\) , \( -2917 a^{3} + 1487 a^{2} + 10926 a - 5648\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-237a^{3}+114a^{2}+898a-459\right){x}-2917a^{3}+1487a^{2}+10926a-5648$ |
| 576.1-a2 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( -\frac{1917985210250720370250}{3} a^{3} + \frac{3705262898043279737500}{3} a^{2} + \frac{513922588181516731250}{3} a - \frac{992822201275698608000}{3} \) |
\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 238 a^{3} + 114 a^{2} - 901 a - 460\) , \( -2679 a^{3} - 1373 a^{2} + 10025 a + 5187\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(238a^{3}+114a^{2}-901a-460\right){x}-2679a^{3}-1373a^{2}+10025a+5187$ |
| 576.1-a3 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$89.96731338$ |
1.874319028 |
\( -\frac{8000}{81} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + 4 a + 1\) , \( 0\) , \( -9 a^{3} + 5 a^{2} + 37 a - 14\) , \( -77 a^{3} + 41 a^{2} + 288 a - 147\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-9a^{3}+5a^{2}+37a-14\right){x}-77a^{3}+41a^{2}+288a-147$ |
| 576.1-a4 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( \frac{2744000}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -58 a^{3} + 29 a^{2} + 218 a - 117\) , \( -387 a^{3} + 204 a^{2} + 1433 a - 743\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-58a^{3}+29a^{2}+218a-117\right){x}-387a^{3}+204a^{2}+1433a-743$ |
| 576.1-a5 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$44.98365669$ |
1.874319028 |
\( \frac{98115010000}{3} a^{3} - 98115010000 a + 46251861000 \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{3} - 3 a\) , \( 50 a^{3} - 150 a - 73\) , \( 4 a^{3} - 12 a - 7\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(50a^{3}-150a-73\right){x}+4a^{3}-12a-7$ |
| 576.1-a6 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$719.7385070$ |
1.874319028 |
\( -\frac{98115010000}{3} a^{3} + 98115010000 a + 46251861000 \) |
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a\) , \( -50 a^{3} + 150 a - 73\) , \( 4 a^{3} - 12 a + 6\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}+\left(-50a^{3}+150a-73\right){x}+4a^{3}-12a+6$ |
| 576.1-a7 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$5.622957086$ |
1.874319028 |
\( \frac{7158018252821364749750}{3} a^{3} - \frac{3705262898043279737500}{3} a^{2} - \frac{26714087801034738628750}{3} a + \frac{13828229390897420342000}{3} \) |
\( \bigl[a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - 3 a\) , \( -50 a^{3} - 114 a^{2} - 37 a - 3\) , \( -742 a^{3} - 1487 a^{2} + 51 a + 300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-50a^{3}-114a^{2}-37a-3\right){x}-742a^{3}-1487a^{2}+51a+300$ |
| 576.1-a8 |
576.1-a |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( -\frac{7158018252821364749750}{3} a^{3} - \frac{3705262898043279737500}{3} a^{2} + \frac{26714087801034738628750}{3} a + \frac{13828229390897420342000}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + 5 a\) , \( 0\) , \( 48 a^{3} - 115 a^{2} + 45 a + 2\) , \( -689 a^{3} + 1423 a^{2} - 38 a - 266\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(48a^{3}-115a^{2}+45a+2\right){x}-689a^{3}+1423a^{2}-38a-266$ |
| 576.1-b1 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( \frac{1917985210250720370250}{3} a^{3} + \frac{3705262898043279737500}{3} a^{2} - \frac{513922588181516731250}{3} a - \frac{992822201275698608000}{3} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( 0\) , \( -237 a^{3} + 115 a^{2} + 900 a - 458\) , \( 2794 a^{3} - 1423 a^{2} - 10487 a + 5426\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-237a^{3}+115a^{2}+900a-458\right){x}+2794a^{3}-1423a^{2}-10487a+5426$ |
| 576.1-b2 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$5.622957086$ |
1.874319028 |
\( -\frac{1917985210250720370250}{3} a^{3} + \frac{3705262898043279737500}{3} a^{2} + \frac{513922588181516731250}{3} a - \frac{992822201275698608000}{3} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{3} - 3 a\) , \( 236 a^{3} + 114 a^{2} - 895 a - 459\) , \( 2917 a^{3} + 1487 a^{2} - 10926 a - 5648\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(236a^{3}+114a^{2}-895a-459\right){x}+2917a^{3}+1487a^{2}-10926a-5648$ |
| 576.1-b3 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$89.96731338$ |
1.874319028 |
\( -\frac{8000}{81} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 0\) , \( -8 a^{3} + 5 a^{2} + 30 a - 16\) , \( 73 a^{3} - 38 a^{2} - 271 a + 140\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-8a^{3}+5a^{2}+30a-16\right){x}+73a^{3}-38a^{2}-271a+140$ |
| 576.1-b4 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( \frac{2744000}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 0\) , \( -10 a^{3} - 29 a^{2} - 16 a + 4\) , \( 75 a^{3} + 129 a^{2} - 57 a - 51\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-10a^{3}-29a^{2}-16a+4\right){x}+75a^{3}+129a^{2}-57a-51$ |
| 576.1-b5 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$719.7385070$ |
1.874319028 |
\( \frac{98115010000}{3} a^{3} - 98115010000 a + 46251861000 \) |
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a\) , \( 50 a^{3} - 150 a - 73\) , \( -4 a^{3} + 12 a + 6\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}+\left(50a^{3}-150a-73\right){x}-4a^{3}+12a+6$ |
| 576.1-b6 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$44.98365669$ |
1.874319028 |
\( -\frac{98115010000}{3} a^{3} + 98115010000 a + 46251861000 \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{3} - 3 a\) , \( -50 a^{3} + 150 a - 73\) , \( -4 a^{3} + 12 a - 7\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-50a^{3}+150a-73\right){x}-4a^{3}+12a-7$ |
| 576.1-b7 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$359.8692535$ |
1.874319028 |
\( \frac{7158018252821364749750}{3} a^{3} - \frac{3705262898043279737500}{3} a^{2} - \frac{26714087801034738628750}{3} a + \frac{13828229390897420342000}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( 0\) , \( a^{2} + a - 2\) , \( -51 a^{3} - 114 a^{2} - 34 a - 4\) , \( 691 a^{3} + 1373 a^{2} - 85 a - 305\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-51a^{3}-114a^{2}-34a-4\right){x}+691a^{3}+1373a^{2}-85a-305$ |
| 576.1-b8 |
576.1-b |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$5.622957086$ |
1.874319028 |
\( -\frac{7158018252821364749750}{3} a^{3} - \frac{3705262898043279737500}{3} a^{2} + \frac{26714087801034738628750}{3} a + \frac{13828229390897420342000}{3} \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{3} - 3 a\) , \( 49 a^{3} - 114 a^{2} + 40 a - 3\) , \( 742 a^{3} - 1487 a^{2} - 51 a + 300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(49a^{3}-114a^{2}+40a-3\right){x}+742a^{3}-1487a^{2}-51a+300$ |
| 576.1-c1 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.675801867$ |
$30.12802380$ |
3.393429123 |
\( \frac{1842168016}{3} a^{2} - \frac{493607432}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 2\) , \( 0\) , \( -a^{2} + 3\) , \( 19 a^{2} - 71\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{2}+3\right){x}+19a^{2}-71$ |
| 576.1-c2 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.337900933$ |
$120.5120952$ |
3.393429123 |
\( \frac{97336}{81} \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+2{x}+1$ |
| 576.1-c3 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.168950466$ |
$964.0967617$ |
3.393429123 |
\( \frac{21952}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( 0\) , \( 0\) , \( -2 a^{3} - 5 a^{2} - 2 a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-2a^{3}-5a^{2}-2a\right){x}$ |
| 576.1-c4 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.337900933$ |
$241.0241904$ |
3.393429123 |
\( \frac{140608}{3} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - 5 a\) , \( 0\) , \( 22 a^{3} + 11 a^{2} - 84 a - 42\) , \( 65 a^{3} + 33 a^{2} - 245 a - 127\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(22a^{3}+11a^{2}-84a-42\right){x}+65a^{3}+33a^{2}-245a-127$ |
| 576.1-c5 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.337900933$ |
$1928.193523$ |
3.393429123 |
\( \frac{7301384}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{3} - 3 a\) , \( -9\) , \( 7\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-9{x}+7$ |
| 576.1-c6 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.675801867$ |
$30.12802380$ |
3.393429123 |
\( -\frac{1842168016}{3} a^{2} + \frac{6875064632}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( 0\) , \( a^{2} - 1\) , \( -19 a^{2} + 5\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{2}-1\right){x}-19a^{2}+5$ |
| 576.1-c7 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.675801867$ |
$964.0967617$ |
3.393429123 |
\( \frac{3625082635210}{3} a^{3} - \frac{18125413176050}{3} a + 2959867576296 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -5 a^{3} - 22 a^{2} - 8 a + 5\) , \( 60 a^{3} + 133 a^{2} - 11 a - 32\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-5a^{3}-22a^{2}-8a+5\right){x}+60a^{3}+133a^{2}-11a-32$ |
| 576.1-c8 |
576.1-c |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.675801867$ |
$964.0967617$ |
3.393429123 |
\( -\frac{3625082635210}{3} a^{3} + \frac{18125413176050}{3} a + 2959867576296 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -28 a^{3} + 21 a^{2} + 104 a - 81\) , \( 230 a^{3} - 134 a^{2} - 861 a + 502\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-28a^{3}+21a^{2}+104a-81\right){x}+230a^{3}-134a^{2}-861a+502$ |
| 576.1-d1 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.310084836$ |
$1028.420087$ |
3.321848692 |
\( \frac{1842168016}{3} a^{2} - \frac{493607432}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( 0\) , \( -a^{2} + 3\) , \( -19 a^{2} + 71\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+3\right){x}-19a^{2}+71$ |
| 576.1-d2 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.620169672$ |
$64.27625544$ |
3.321848692 |
\( \frac{97336}{81} \) |
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( 0\) , \( 2\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}-{x}^{2}+2{x}-1$ |
| 576.1-d3 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.310084836$ |
$514.2100435$ |
3.321848692 |
\( \frac{21952}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} + a + 2\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + a + 2\) , \( -8 a^{3} - 17 a^{2} - a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-3a^{3}-5a^{2}+a+2\right){x}-8a^{3}-17a^{2}-a+3$ |
| 576.1-d4 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.155042418$ |
$2056.840174$ |
3.321848692 |
\( \frac{140608}{3} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -4 a^{3} - 11 a^{2} - 6 a - 1\) , \( 11 a^{3} + 22 a^{2} - a - 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-4a^{3}-11a^{2}-6a-1\right){x}+11a^{3}+22a^{2}-a-5$ |
| 576.1-d5 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$0.620169672$ |
$64.27625544$ |
3.321848692 |
\( \frac{7301384}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a\) , \( -9\) , \( -8\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}-9{x}-8$ |
| 576.1-d6 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.310084836$ |
$1028.420087$ |
3.321848692 |
\( -\frac{1842168016}{3} a^{2} + \frac{6875064632}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 1\) , \( 0\) , \( a^{2} - 1\) , \( 19 a^{2} - 5\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{2}-1\right){x}+19a^{2}-5$ |
| 576.1-d7 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1.240339345$ |
$8.034531930$ |
3.321848692 |
\( \frac{3625082635210}{3} a^{3} - \frac{18125413176050}{3} a + 2959867576296 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -7 a^{3} - 20 a^{2} - 2 a + 2\) , \( -65 a^{3} - 154 a^{2} + 2 a + 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-7a^{3}-20a^{2}-2a+2\right){x}-65a^{3}-154a^{2}+2a+33$ |
| 576.1-d8 |
576.1-d |
$8$ |
$16$ |
\(\Q(\zeta_{24})^+\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{2} \) |
$9.49364$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1.240339345$ |
$8.034531930$ |
3.321848692 |
\( -\frac{3625082635210}{3} a^{3} + \frac{18125413176050}{3} a + 2959867576296 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{2} + a - 2\) , \( -28 a^{3} + 19 a^{2} + 106 a - 76\) , \( -259 a^{3} + 154 a^{2} + 969 a - 583\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-28a^{3}+19a^{2}+106a-76\right){x}-259a^{3}+154a^{2}+969a-583$ |
*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.
