| 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 |
| 512.2-a1 |
512.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( -1088 a + 2816 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a + 2\) , \( 2 a + 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a+2\right){x}+2a+3$ |
| 512.2-a2 |
512.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( -53387236 a + 136758060 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 75 a - 191\) , \( -546 a + 1398\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(75a-191\right){x}-546a+1398$ |
| 512.2-a3 |
512.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$33.31209033$ |
2.019842162 |
\( 1008 a + 17168 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 5 a - 11\) , \( -10 a + 26\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(5a-11\right){x}-10a+26$ |
| 512.2-a4 |
512.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( 87515172 a + 136659620 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 9\) , \( -30 a + 78\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+9\right){x}-30a+78$ |
| 512.2-b1 |
512.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.495413934$ |
$11.52843721$ |
2.770410930 |
\( -404500 a + 1037028 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 136 a - 344\) , \( -1200 a + 3072\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(136a-344\right){x}-1200a+3072$ |
| 512.2-b2 |
512.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.990827869$ |
$23.05687443$ |
2.770410930 |
\( 240 a + 2576 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 24\) , \( -10 a + 24\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-24\right){x}-10a+24$ |
| 512.2-b3 |
512.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{13} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.495413934$ |
$23.05687443$ |
2.770410930 |
\( 6168 a + 10976 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+{x}$ |
| 512.2-b4 |
512.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.981655739$ |
$5.764218608$ |
2.770410930 |
\( 1335292 a + 2147084 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 81 a - 204\) , \( 568 a - 1456\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(81a-204\right){x}+568a-1456$ |
| 512.2-c1 |
512.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.16812741$ |
1.839405631 |
\( -23360 a + 59136 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 9\) , \( 6 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-9\right){x}+6a-14$ |
| 512.2-c2 |
512.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.16812741$ |
1.839405631 |
\( 414800 a + 647728 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 24\) , \( 510 a - 1308\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-24\right){x}+510a-1308$ |
| 512.2-d1 |
512.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( 184 a + 560 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 5\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a+5\right){x}+2a-6$ |
| 512.2-d2 |
512.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.01940372$ |
1.942638047 |
\( -1092 a + 5588 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -9 a - 12\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-12\right){x}-8a-12$ |
| 512.2-d3 |
512.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( -10297338 a + 26411786 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -59 a - 92\) , \( 378 a + 588\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a-92\right){x}+378a+588$ |
| 512.2-d4 |
512.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( 910322 a + 1430310 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -124 a - 192\) , \( -1012 a - 1580\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-124a-192\right){x}-1012a-1580$ |
| 512.2-e1 |
512.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.239280630$ |
1.513247827 |
\( -\frac{217}{16} a - \frac{339}{16} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -8 a + 20\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-8a+20$ |
| 512.2-e2 |
512.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$12.47856126$ |
1.513247827 |
\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a - 168\) , \( 192 a + 304\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a-168\right){x}+192a+304$ |
| 512.2-e3 |
512.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.47856126$ |
1.513247827 |
\( \frac{159495}{4} a + \frac{481229}{4} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a - 108\) , \( -374 a - 584\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a-108\right){x}-374a-584$ |
| 512.2-e4 |
512.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.119640315$ |
1.513247827 |
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 768 a - 1968\) , \( 7764 a - 19888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(768a-1968\right){x}+7764a-19888$ |
| 512.2-f1 |
512.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.235830817$ |
$12.22307372$ |
2.796510914 |
\( -\frac{217}{16} a - \frac{339}{16} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 7\) , \( 50 a + 78\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a-7\right){x}+50a+78$ |
| 512.2-f2 |
512.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.235830817$ |
$12.22307372$ |
2.796510914 |
\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 90 a - 235\) , \( -633 a + 1626\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(90a-235\right){x}-633a+1626$ |
| 512.2-f3 |
512.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.471661635$ |
$24.44614744$ |
2.796510914 |
\( \frac{159495}{4} a + \frac{481229}{4} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 15\) , \( -6 a + 22\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(5a-15\right){x}-6a+22$ |
| 512.2-f4 |
512.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.943323270$ |
$12.22307372$ |
2.796510914 |
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 55\) , \( 90 a + 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-55\right){x}+90a+54$ |
| 512.2-g1 |
512.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.156172055$ |
$9.650305188$ |
2.706070181 |
\( 184 a + 560 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+8\right){x}$ |
| 512.2-g2 |
512.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.578086027$ |
$19.30061037$ |
2.706070181 |
\( -1092 a + 5588 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 4\) , \( 2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-4\right){x}+2a-4$ |
| 512.2-g3 |
512.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.156172055$ |
$4.825152594$ |
2.706070181 |
\( -10297338 a + 26411786 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a - 84\) , \( 140 a - 364\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-84\right){x}+140a-364$ |
| 512.2-g4 |
512.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.289043013$ |
$19.30061037$ |
2.706070181 |
\( 910322 a + 1430310 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( -20 a + 52\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-24\right){x}-20a+52$ |
| 512.2-h1 |
512.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.818306195$ |
$6.640608214$ |
2.635901835 |
\( -23360 a + 59136 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a - 9\) , \( -22 a - 34\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-9\right){x}-22a-34$ |
| 512.2-h2 |
512.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.636612390$ |
$6.640608214$ |
2.635901835 |
\( 414800 a + 647728 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( -4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}-4$ |
| 512.2-i1 |
512.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.399642117$ |
$14.24941430$ |
2.762318808 |
\( -404500 a + 1037028 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+4a{x}+16$ |
| 512.2-i2 |
512.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.799284235$ |
$28.49882861$ |
2.762318808 |
\( 240 a + 2576 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 512.2-i3 |
512.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{13} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.598568471$ |
$14.24941430$ |
2.762318808 |
\( 6168 a + 10976 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a + 38\) , \( -15 a + 39\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-14a+38\right){x}-15a+39$ |
| 512.2-i4 |
512.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.399642117$ |
$14.24941430$ |
2.762318808 |
\( 1335292 a + 2147084 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a - 20\) , \( 26 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a-20\right){x}+26a+40$ |
| 512.2-j1 |
512.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.62255413$ |
1.288173903 |
\( -1088 a + 2816 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 15\) , \( 7 a - 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(6a-15\right){x}+7a-18$ |
| 512.2-j2 |
512.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$21.24510827$ |
1.288173903 |
\( -53387236 a + 136758060 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( 20 a + 36\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-28\right){x}+20a+36$ |
| 512.2-j3 |
512.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$21.24510827$ |
1.288173903 |
\( 1008 a + 17168 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -18 a - 28\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-8\right){x}-18a-28$ |
| 512.2-j4 |
512.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.2 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.311277067$ |
1.288173903 |
\( 87515172 a + 136659620 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a - 148\) , \( -848 a - 1324\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a-148\right){x}-848a-1324$ |
*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.
