| 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 |
| 576.3-a1 |
576.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$13.68670407$ |
1.191274681 |
\( -16848 a + 58752 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 12\) , \( -3 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-3a-12\right){x}-3a-3$ |
| 576.3-a2 |
576.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.562234692$ |
1.191274681 |
\( -155578800 a + 524686128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 28 a - 92\) , \( 147 a - 496\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a-92\right){x}+147a-496$ |
| 576.3-a3 |
576.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$13.68670407$ |
1.191274681 |
\( 16848 a + 41904 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1797 a - 4263\) , \( 69657 a + 165246\bigr] \) |
${y}^2={x}^{3}+\left(-1797a-4263\right){x}+69657a+165246$ |
| 576.3-a4 |
576.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.562234692$ |
1.191274681 |
\( 155578800 a + 369107328 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1454 a - 4897\) , \( 50298 a - 169622\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1454a-4897\right){x}+50298a-169622$ |
| 576.3-b1 |
576.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.187165905$ |
2.186676077 |
\( \frac{38912}{27} a - \frac{131072}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 87 a + 207\) , \( 13071 a + 31008\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(87a+207\right){x}+13071a+31008$ |
| 576.3-b2 |
576.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.187165905$ |
2.186676077 |
\( -\frac{126738464}{9} a + \frac{427666096}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4143 a - 9828\) , \( 232824 a + 552324\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4143a-9828\right){x}+232824a+552324$ |
| 576.3-c1 |
576.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$1.775052230$ |
0.926990794 |
\( -93184 a - 221184 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -923 a - 2189\) , \( -27299 a - 64761\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-923a-2189\right){x}-27299a-64761$ |
| 576.3-d1 |
576.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.975815635$ |
2.063672126 |
\( -\frac{11583}{16} a - \frac{999}{2} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -492 a - 1167\) , \( -12684 a - 30090\bigr] \) |
${y}^2={x}^{3}+\left(-492a-1167\right){x}-12684a-30090$ |
| 576.3-d2 |
576.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.927446905$ |
2.063672126 |
\( \frac{42964449}{4096} a - \frac{17445543}{512} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 141 a - 468\) , \( -1484 a + 5000\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(141a-468\right){x}-1484a+5000$ |
| 576.3-d3 |
576.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.85489381$ |
2.063672126 |
\( -\frac{39704429193}{64} a + \frac{16736831295}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4882 a - 11581\) , \( 161034 a + 382018\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4882a-11581\right){x}+161034a+382018$ |
| 576.3-d4 |
576.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.951631270$ |
2.063672126 |
\( \frac{9185319}{4} a + 5449950 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 48\) , \( -39 a - 39\bigr] \) |
${y}^2={x}^{3}+\left(-3a-48\right){x}-39a-39$ |
| 576.3-e1 |
576.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.456199331$ |
1.520950597 |
\( \frac{29360}{243} a - \frac{136832}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a - 25\) , \( -106 a - 254\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-25\right){x}-106a-254$ |
| 576.3-e2 |
576.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{11} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.912398663$ |
1.520950597 |
\( -\frac{8211472}{27} a + \frac{38838416}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14958 a - 35484\) , \( -1662501 a - 3943920\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14958a-35484\right){x}-1662501a-3943920$ |
| 576.3-f1 |
576.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.566074309$ |
$7.590114827$ |
4.138412119 |
\( 96 a + 240 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 369 a + 876\) , \( 9896 a + 23476\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(369a+876\right){x}+9896a+23476$ |
| 576.3-f2 |
576.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.783037154$ |
$15.18022965$ |
4.138412119 |
\( -3588 a + 16608 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-5\right){x}$ |
| 576.3-g1 |
576.3-g |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$15.15896031$ |
2.638836277 |
\( -93184 a - 221184 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 13\) , \( -35 a + 119\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-13\right){x}-35a+119$ |
| 576.3-h1 |
576.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.398149169$ |
$9.328485208$ |
3.879280844 |
\( 96 a + 240 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$ |
| 576.3-h2 |
576.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.199074584$ |
$18.65697041$ |
3.879280844 |
\( -3588 a + 16608 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 326 a - 1093\) , \( -5364 a + 18092\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(326a-1093\right){x}-5364a+18092$ |
| 576.3-i1 |
576.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.418710952$ |
1.291431812 |
\( \frac{38912}{27} a - \frac{131072}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 7 a - 17\) , \( -17 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-17\right){x}-17a+60$ |
| 576.3-i2 |
576.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.418710952$ |
1.291431812 |
\( -\frac{126738464}{9} a + \frac{427666096}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 97 a - 332\) , \( -944 a + 3156\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(97a-332\right){x}-944a+3156$ |
| 576.3-j1 |
576.3-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.418534733$ |
1.538336338 |
\( -\frac{11583}{16} a - \frac{999}{2} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a + 201\) , \( 276 a - 930\bigr] \) |
${y}^2={x}^{3}+\left(-60a+201\right){x}+276a-930$ |
| 576.3-j2 |
576.3-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.472844911$ |
1.538336338 |
\( \frac{42964449}{4096} a - \frac{17445543}{512} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 413 a + 980\) , \( -5028 a - 11928\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(413a+980\right){x}-5028a-11928$ |
| 576.3-j3 |
576.3-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.945689822$ |
1.538336338 |
\( -\frac{39704429193}{64} a + \frac{16736831295}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 54 a - 189\) , \( 406 a - 1362\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(54a-189\right){x}+406a-1362$ |
| 576.3-j4 |
576.3-j |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.837069466$ |
1.538336338 |
\( \frac{9185319}{4} a + 5449950 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15045 a - 50736\) , \( 905541 a - 3053739\bigr] \) |
${y}^2={x}^{3}+\left(15045a-50736\right){x}+905541a-3053739$ |
| 576.3-k1 |
576.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.955705096$ |
2.421665677 |
\( \frac{29360}{243} a - \frac{136832}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 702 a - 2361\) , \( -29502 a + 99486\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(702a-2361\right){x}-29502a+99486$ |
| 576.3-k2 |
576.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{11} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$13.91141019$ |
2.421665677 |
\( -\frac{8211472}{27} a + \frac{38838416}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 68\) , \( -25 a + 240\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-68\right){x}-25a+240$ |
| 576.3-l1 |
576.3-l |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$8.182060030$ |
2.136470746 |
\( -16848 a + 58752 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1797 a - 6060\) , \( 69657 a - 234903\bigr] \) |
${y}^2={x}^{3}+\left(1797a-6060\right){x}+69657a-234903$ |
| 576.3-l2 |
576.3-l |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$24.54618009$ |
2.136470746 |
\( -155578800 a + 524686128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1452 a - 3444\) , \( 51751 a + 122768\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1452a-3444\right){x}+51751a+122768$ |
| 576.3-l3 |
576.3-l |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$8.182060030$ |
2.136470746 |
\( 16848 a + 41904 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 15\) , \( -3 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(3a-15\right){x}-3a+6$ |
| 576.3-l4 |
576.3-l |
$4$ |
$6$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.51479$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$24.54618009$ |
2.136470746 |
\( 155578800 a + 369107328 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -26 a - 65\) , \( 174 a + 414\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a-65\right){x}+174a+414$ |
*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.
