| 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 |
| 512.1-a1 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( -87515172 a + 224174792 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a + 4\) , \( 30 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+4\right){x}+30a+48$ |
| 512.1-a2 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( 1088 a + 1728 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 3\) , \( -2 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}-2a+5$ |
| 512.1-a3 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$33.31209033$ |
2.019842162 |
\( -1008 a + 18176 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -5 a - 6\) , \( 10 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-6\right){x}+10a+16$ |
| 512.1-a4 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.65604516$ |
2.019842162 |
\( 53387236 a + 83370824 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -75 a - 116\) , \( 546 a + 852\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-75a-116\right){x}+546a+852$ |
| 512.1-b1 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{13} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.495413934$ |
$23.05687443$ |
2.770410930 |
\( -6168 a + 17144 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2a{x}-a$ |
| 512.1-b2 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.990827869$ |
$23.05687443$ |
2.770410930 |
\( -240 a + 2816 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9 a - 14\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-14\right){x}$ |
| 512.1-b3 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.981655739$ |
$5.764218608$ |
2.770410930 |
\( -1335292 a + 3482376 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -79 a - 124\) , \( -648 a - 1012\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a-124\right){x}-648a-1012$ |
| 512.1-b4 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.495413934$ |
$11.52843721$ |
2.770410930 |
\( 404500 a + 632528 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -134 a - 209\) , \( 1065 a + 1663\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-134a-209\right){x}+1065a+1663$ |
| 512.1-c1 |
512.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.16812741$ |
1.839405631 |
\( -414800 a + 1062528 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9 a - 14\) , \( -520 a - 812\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-14\right){x}-520a-812$ |
| 512.1-c2 |
512.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.16812741$ |
1.839405631 |
\( 23360 a + 35776 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 5\) , \( -2 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-5\right){x}-2a-3$ |
| 512.1-d1 |
512.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( -184 a + 744 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 4\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+4\right){x}-2a-4$ |
| 512.1-d2 |
512.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.01940372$ |
1.942638047 |
\( 1092 a + 4496 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 9 a - 21\) , \( 8 a - 20\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(9a-21\right){x}+8a-20$ |
| 512.1-d3 |
512.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( -910322 a + 2340632 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 124 a - 316\) , \( 1012 a - 2592\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(124a-316\right){x}+1012a-2592$ |
| 512.1-d4 |
512.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.009701860$ |
1.942638047 |
\( 10297338 a + 16114448 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 59 a - 151\) , \( -378 a + 966\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(59a-151\right){x}-378a+966$ |
| 512.1-e1 |
512.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.239280630$ |
1.513247827 |
\( \frac{217}{16} a - \frac{139}{4} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 8 a + 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+8a+12$ |
| 512.1-e2 |
512.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.119640315$ |
1.513247827 |
\( -\frac{23841914775}{2} a + 30536164178 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -768 a - 1200\) , \( -7764 a - 12124\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-768a-1200\right){x}-7764a-12124$ |
| 512.1-e3 |
512.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.47856126$ |
1.513247827 |
\( -\frac{159495}{4} a + 160181 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 71 a - 178\) , \( 444 a - 1136\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(71a-178\right){x}+444a-1136$ |
| 512.1-e4 |
512.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$12.47856126$ |
1.513247827 |
\( \frac{1592342311}{2} a + 1243265046 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 106 a - 273\) , \( -87 a + 223\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(106a-273\right){x}-87a+223$ |
| 512.1-f1 |
512.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.235830817$ |
$12.22307372$ |
2.796510914 |
\( \frac{217}{16} a - \frac{139}{4} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 12\) , \( -50 a + 128\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-12\right){x}-50a+128$ |
| 512.1-f2 |
512.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.943323270$ |
$12.22307372$ |
2.796510914 |
\( -\frac{23841914775}{2} a + 30536164178 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 60\) , \( -90 a + 144\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-60\right){x}-90a+144$ |
| 512.1-f3 |
512.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.471661635$ |
$24.44614744$ |
2.796510914 |
\( -\frac{159495}{4} a + 160181 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a - 10\) , \( 6 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-10\right){x}+6a+16$ |
| 512.1-f4 |
512.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.235830817$ |
$12.22307372$ |
2.796510914 |
\( \frac{1592342311}{2} a + 1243265046 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -90 a - 145\) , \( 633 a + 993\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-90a-145\right){x}+633a+993$ |
| 512.1-g1 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.156172055$ |
$9.650305188$ |
2.706070181 |
\( -184 a + 744 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a + 12\) , \( -4 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+12\right){x}-4a+12$ |
| 512.1-g2 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.578086027$ |
$19.30061037$ |
2.706070181 |
\( 1092 a + 4496 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}$ |
| 512.1-g3 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.289043013$ |
$19.30061037$ |
2.706070181 |
\( -910322 a + 2340632 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 17\) , \( 27 a + 49\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}+27a+49$ |
| 512.1-g4 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.156172055$ |
$4.825152594$ |
2.706070181 |
\( 10297338 a + 16114448 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a - 52\) , \( -108 a - 172\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a-52\right){x}-108a-172$ |
| 512.1-h1 |
512.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.636612390$ |
$6.640608214$ |
2.635901835 |
\( -414800 a + 1062528 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 1\) , \( -4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a-1\right){x}-4$ |
| 512.1-h2 |
512.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.818306195$ |
$6.640608214$ |
2.635901835 |
\( 23360 a + 35776 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 16\) , \( 22 a - 56\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7a-16\right){x}+22a-56$ |
| 512.1-i1 |
512.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{13} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.598568471$ |
$14.24941430$ |
2.762318808 |
\( -6168 a + 17144 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 14 a + 24\) , \( 15 a + 24\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a+24\right){x}+15a+24$ |
| 512.1-i2 |
512.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.799284235$ |
$28.49882861$ |
2.762318808 |
\( -240 a + 2816 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a-1\right){x}$ |
| 512.1-i3 |
512.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.399642117$ |
$14.24941430$ |
2.762318808 |
\( -1335292 a + 3482376 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 31\) , \( -26 a + 66\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-31\right){x}-26a+66$ |
| 512.1-i4 |
512.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.399642117$ |
$14.24941430$ |
2.762318808 |
\( 404500 a + 632528 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4 a + 4\) , \( 16\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-4a+4\right){x}+16$ |
| 512.1-j1 |
512.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.311277067$ |
1.288173903 |
\( -87515172 a + 224174792 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 97 a - 244\) , \( 752 a - 1928\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(97a-244\right){x}+752a-1928$ |
| 512.1-j2 |
512.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.62255413$ |
1.288173903 |
\( 1088 a + 1728 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6 a - 9\) , \( -7 a - 11\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-6a-9\right){x}-7a-11$ |
| 512.1-j3 |
512.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{14} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$21.24510827$ |
1.288173903 |
\( -1008 a + 18176 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 7 a - 14\) , \( 12 a - 32\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-14\right){x}+12a-32$ |
| 512.1-j4 |
512.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$21.24510827$ |
1.288173903 |
\( 53387236 a + 83370824 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 44\) , \( -36 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-44\right){x}-36a+100$ |
*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.
