| 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 |
| 324.1-a1 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{5} \cdot 3^{22} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( -\frac{718857823406363308019}{3888} a + \frac{1841392279556091303607}{3888} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 17223 a - 45792\) , \( -1827113 a + 4707820\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(17223a-45792\right){x}-1827113a+4707820$ |
| 324.1-a2 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{25} \cdot 3^{14} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( -\frac{3440210411}{3145728} a + \frac{8999174503}{3145728} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 33 a - 72\) , \( -131 a + 244\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(33a-72\right){x}-131a+244$ |
| 324.1-a3 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{25} \cdot 3^{14} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( \frac{3440210411}{3145728} a + \frac{1389741023}{786432} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -33 a - 39\) , \( 131 a + 113\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-33a-39\right){x}+131a+113$ |
| 324.1-a4 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( \frac{141420761}{9216} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1563 a - 4005\) , \( 45119 a - 115575\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1563a-4005\right){x}+45119a-115575$ |
| 324.1-a5 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{52} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.581253140$ |
0.563898374 |
\( \frac{211293405175481}{6973568802} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 178683 a - 457875\) , \( -57387877 a + 147002943\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(178683a-457875\right){x}-57387877a+147002943$ |
| 324.1-a6 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{20} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.581253140$ |
0.563898374 |
\( \frac{551569744601}{2592} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24603 a - 38442\) , \( -3010943 a - 4701784\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-24603a-38442\right){x}-3010943a-4701784$ |
| 324.1-a7 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{32} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B.4.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( \frac{206226044828441}{236196} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -177243 a - 276942\) , \( 58383673 a + 91170068\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-177243a-276942\right){x}+58383673a+91170068$ |
| 324.1-a8 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{5} \cdot 3^{22} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325012561$ |
0.563898374 |
\( \frac{718857823406363308019}{3888} a + \frac{280633614037431998897}{972} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -17223 a - 28569\) , \( 1827113 a + 2880707\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-17223a-28569\right){x}+1827113a+2880707$ |
| 324.1-b1 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.740155267$ |
3.798446809 |
\( -\frac{8246475}{4} a + \frac{21114837}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 a - 56\) , \( -162 a - 269\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27a-56\right){x}-162a-269$ |
| 324.1-b2 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$15.66139740$ |
3.798446809 |
\( -\frac{21681}{64} a + \frac{128925}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a + 4\) , \( 2 a + 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a+4\right){x}+2a+3$ |
| 324.1-b3 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$15.66139740$ |
3.798446809 |
\( \frac{21681}{64} a + \frac{26811}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a + 7\) , \( -2 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a+7\right){x}-2a+5$ |
| 324.1-b4 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.740155267$ |
3.798446809 |
\( \frac{8246475}{4} a + \frac{6434181}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 a - 83\) , \( 162 a - 431\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(27a-83\right){x}+162a-431$ |
| 324.1-c1 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{14} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.423156397$ |
$1.874367958$ |
2.587873310 |
\( -\frac{5106375}{4096} a + \frac{2467125}{1024} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a - 110\) , \( -777 a - 1215\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-68a-110\right){x}-777a-1215$ |
| 324.1-c2 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{10} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.474385465$ |
$16.86931162$ |
2.587873310 |
\( -\frac{30337875}{64} a + \frac{77749875}{64} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a + 10\) , \( 18 a + 29\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a+10\right){x}+18a+29$ |
| 324.1-c3 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{14} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.237192732$ |
$16.86931162$ |
2.587873310 |
\( \frac{5106375}{4096} a + \frac{4762125}{4096} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a - 20\) , \( -32 a + 79\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a-20\right){x}-32a+79$ |
| 324.1-c4 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{10} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.711578198$ |
$1.874367958$ |
2.587873310 |
\( \frac{30337875}{64} a + \frac{1481625}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a + 160\) , \( 573 a - 1485\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-68a+160\right){x}+573a-1485$ |
| 324.1-d1 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$33.66333849$ |
0.907173204 |
\( -\frac{8246475}{4} a + \frac{21114837}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a - 6\) , \( 7 a + 12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a-6\right){x}+7a+12$ |
| 324.1-d2 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.740370943$ |
0.907173204 |
\( -\frac{21681}{64} a + \frac{128925}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a + 39\) , \( -81 a - 127\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a+39\right){x}-81a-127$ |
| 324.1-d3 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.740370943$ |
0.907173204 |
\( \frac{21681}{64} a + \frac{26811}{16} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a + 66\) , \( 81 a - 208\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a+66\right){x}+81a-208$ |
| 324.1-d4 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$33.66333849$ |
0.907173204 |
\( \frac{8246475}{4} a + \frac{6434181}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 9\) , \( -7 a + 19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a-9\right){x}-7a+19$ |
| 324.1-e1 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{27} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -81 a + 202\) , \( -2862 a + 7337\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-81a+202\right){x}-2862a+7337$ |
| 324.1-e2 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9 a - 14\) , \( -108 a - 169\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-9a-14\right){x}-108a-169$ |
| 324.1-e3 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{27} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 81 a + 121\) , \( 2862 a + 4475\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(81a+121\right){x}+2862a+4475$ |
| 324.1-e4 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 23\) , \( 108 a - 277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9a-23\right){x}+108a-277$ |
| 324.1-e5 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$7.891158903$ |
3.827774313 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9 a - 17\) , \( 4 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-9a-17\right){x}+4a+5$ |
| 324.1-e6 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 8829 a - 22661\) , \( -651802 a + 1669545\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(8829a-22661\right){x}-651802a+1669545$ |
| 324.1-e7 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$7.891158903$ |
3.827774313 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 549 a - 1421\) , \( -10282 a + 26361\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(549a-1421\right){x}-10282a+26361$ |
| 324.1-e8 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$7.891158903$ |
3.827774313 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 26\) , \( -4 a + 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9a-26\right){x}-4a+9$ |
| 324.1-e9 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -99 a - 197\) , \( 940 a + 1373\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-99a-197\right){x}+940a+1373$ |
| 324.1-e10 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$7.891158903$ |
3.827774313 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -549 a - 872\) , \( 10282 a + 16079\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-549a-872\right){x}+10282a+16079$ |
| 324.1-e11 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 99 a - 296\) , \( -940 a + 2313\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(99a-296\right){x}-940a+2313$ |
| 324.1-e12 |
324.1-e |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{12} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.945579451$ |
3.827774313 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -8829 a - 13832\) , \( 651802 a + 1017743\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8829a-13832\right){x}+651802a+1017743$ |
| 324.1-f1 |
324.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{14} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.237192732$ |
$16.86931162$ |
2.587873310 |
\( -\frac{5106375}{4096} a + \frac{2467125}{1024} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a - 12\) , \( 31 a + 48\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a-12\right){x}+31a+48$ |
| 324.1-f2 |
324.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{10} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.711578198$ |
$1.874367958$ |
2.587873310 |
\( -\frac{30337875}{64} a + \frac{77749875}{64} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a + 93\) , \( -574 a - 911\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(67a+93\right){x}-574a-911$ |
| 324.1-f3 |
324.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{14} \cdot 3^{18} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.423156397$ |
$1.874367958$ |
2.587873310 |
\( \frac{5106375}{4096} a + \frac{4762125}{4096} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a - 177\) , \( 776 a - 1991\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(67a-177\right){x}+776a-1991$ |
| 324.1-f4 |
324.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{10} \cdot 3^{6} \) |
$1.56315$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.474385465$ |
$16.86931162$ |
2.587873310 |
\( \frac{30337875}{64} a + \frac{1481625}{2} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a + 18\) , \( -19 a + 48\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a+18\right){x}-19a+48$ |
*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.
