| 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 |
| 512.3-a1 |
512.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{10} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.02256012$ |
1.821753004 |
\( -1088 a + 2816 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
| 512.3-a2 |
512.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$15.02256012$ |
1.821753004 |
\( -53387236 a + 136758060 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 64\) , \( -108 a + 284\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-64\right){x}-108a+284$ |
| 512.3-a3 |
512.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$15.02256012$ |
1.821753004 |
\( 1008 a + 17168 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -4 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-4{x}-4a+4$ |
| 512.3-a4 |
512.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.755640031$ |
1.821753004 |
\( 87515172 a + 136659620 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 24\) , \( -76 a - 100\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-24\right){x}-76a-100$ |
| 512.3-b1 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{21} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.54946238$ |
2.128184914 |
\( -774198 a + 1983150 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a + 17\) , \( 1218 a + 1902\bigr] \) |
${y}^2={x}^{3}+\left(11a+17\right){x}+1218a+1902$ |
| 512.3-b2 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{27} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.193682798$ |
2.128184914 |
\( -349618194 a + 895566564 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 167 a + 257\) , \( -1270 a - 1986\bigr] \) |
${y}^2={x}^{3}+\left(167a+257\right){x}-1270a-1986$ |
| 512.3-b3 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{24} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$8.774731193$ |
2.128184914 |
\( -8748 a + 25056 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -53 a - 83\) , \( -178 a - 278\bigr] \) |
${y}^2={x}^{3}+\left(-53a-83\right){x}-178a-278$ |
| 512.3-b4 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{24} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$17.54946238$ |
2.128184914 |
\( 8748 a + 16308 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 7\) , \( 2 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-7\right){x}+2a+6$ |
| 512.3-b5 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{21} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.387365596$ |
2.128184914 |
\( 774198 a + 1208952 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 2\) , \( 3 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-2a-2\right){x}+3a-15$ |
| 512.3-b6 |
512.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{27} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.774731193$ |
2.128184914 |
\( 349618194 a + 545948370 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -41 a - 47\) , \( 170 a + 286\bigr] \) |
${y}^2={x}^{3}+\left(-41a-47\right){x}+170a+286$ |
| 512.3-c1 |
512.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$6.823796239$ |
1.655013686 |
\( 184 a + 560 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+4{x}$ |
| 512.3-c2 |
512.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$13.64759247$ |
1.655013686 |
\( -1092 a + 5588 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 44 a - 112\) , \( 164 a - 420\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(44a-112\right){x}+164a-420$ |
| 512.3-c3 |
512.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.411898119$ |
1.655013686 |
\( -10297338 a + 26411786 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 684 a - 1752\) , \( 13412 a - 34356\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(684a-1752\right){x}+13412a-34356$ |
| 512.3-c4 |
512.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$27.29518495$ |
1.655013686 |
\( 910322 a + 1430310 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a - 15\) , \( 32 a + 50\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-9a-15\right){x}+32a+50$ |
| 512.3-d1 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.322084795$ |
$8.484451650$ |
2.720562010 |
\( -292271882500 a + 748669862250 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -25 a - 148\) , \( 525 a + 1296\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-25a-148\right){x}+525a+1296$ |
| 512.3-d2 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.661042397$ |
$8.484451650$ |
2.720562010 |
\( -20500 a + 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 31 a - 75\) , \( 132 a - 340\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(31a-75\right){x}+132a-340$ |
| 512.3-d3 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.330521198$ |
$16.96890330$ |
2.720562010 |
\( 2000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a - 8\) , \( 5 a + 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a-8\right){x}+5a+8$ |
| 512.3-d4 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.661042397$ |
$8.484451650$ |
2.720562010 |
\( 20500 a + 33500 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a + 12\) , \( -5 a + 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-5a+12\right){x}-5a+12$ |
| 512.3-d5 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.661042397$ |
$16.96890330$ |
2.720562010 |
\( 1098500 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -65 a - 108\) , \( 445 a + 704\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-65a-108\right){x}+445a+704$ |
| 512.3-d6 |
512.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.322084795$ |
$8.484451650$ |
2.720562010 |
\( 292271882500 a + 456397979750 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1065 a - 1668\) , \( 27565 a + 43056\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1065a-1668\right){x}+27565a+43056$ |
| 512.3-e1 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( -7659605 a + 19620476 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 9 a - 22\) , \( 18 a - 39\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(9a-22\right){x}+18a-39$ |
| 512.3-e2 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -12 a + 32\) , \( -92 a + 236\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a+32\right){x}-92a+236$ |
| 512.3-e3 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-8\right){x}$ |
| 512.3-e4 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 94 a - 239\) , \( 655 a - 1678\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(94a-239\right){x}+655a-1678$ |
| 512.3-e5 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -44 a - 128\) , \( -352 a - 416\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-44a-128\right){x}-352a-416$ |
| 512.3-e6 |
512.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( 2701312025 a + 4218241728 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -166 a + 421\) , \( 3275 a - 8378\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-166a+421\right){x}+3275a-8378$ |
| 512.3-f1 |
512.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.548841397$ |
$20.15171496$ |
2.682467151 |
\( -404500 a + 1037028 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a + 20\) , \( 46 a + 72\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(13a+20\right){x}+46a+72$ |
| 512.3-f2 |
512.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.274420698$ |
$20.15171496$ |
2.682467151 |
\( 240 a + 2576 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3 a - 8\) , \( -3 a + 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3a-8\right){x}-3a+8$ |
| 512.3-f3 |
512.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.548841397$ |
$10.07585748$ |
2.682467151 |
\( 6168 a + 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a - 15\) , \( -27 a - 42\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-10a-15\right){x}-27a-42$ |
| 512.3-f4 |
512.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.548841397$ |
$10.07585748$ |
2.682467151 |
\( 1335292 a + 2147084 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 23 a - 68\) , \( 93 a - 224\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(23a-68\right){x}+93a-224$ |
| 512.3-g1 |
512.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{16} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.30367226$ |
1.977110671 |
\( -404500 a + 1037028 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 15\) , \( -16 a + 42\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7a-15\right){x}-16a+42$ |
| 512.3-g2 |
512.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.30367226$ |
1.977110671 |
\( 240 a + 2576 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 15\) , \( -9 a - 14\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-15\right){x}-9a-14$ |
| 512.3-g3 |
512.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{19} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.30367226$ |
1.977110671 |
\( 6168 a + 10976 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a+13\right){x}$ |
| 512.3-g4 |
512.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.075918066$ |
1.977110671 |
\( 1335292 a + 2147084 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -150 a - 235\) , \( -1317 a - 2058\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-150a-235\right){x}-1317a-2058$ |
| 512.3-h1 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.265147111$ |
1.583828990 |
\( -7659605 a + 19620476 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -17 a - 27\) , \( -990 a - 1546\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-17a-27\right){x}-990a-1546$ |
| 512.3-h2 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.530294222$ |
1.583828990 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7 a + 12\) , \( 7 a + 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(7a+12\right){x}+7a+12$ |
| 512.3-h3 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$13.06058844$ |
1.583828990 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 64 a - 160\) , \( -368 a + 944\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(64a-160\right){x}-368a+944$ |
| 512.3-h4 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.530294222$ |
1.583828990 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 12\) , \( -4 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-12\right){x}-4a-12$ |
| 512.3-h5 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.06058844$ |
1.583828990 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 984 a - 2520\) , \( -24304 a + 62256\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(984a-2520\right){x}-24304a+62256$ |
| 512.3-h6 |
512.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.632573555$ |
1.583828990 |
\( 2701312025 a + 4218241728 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a - 152\) , \( -684 a - 1092\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a-152\right){x}-684a-1092$ |
| 512.3-i1 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$3.068055274$ |
$3.832786753$ |
2.852025313 |
\( -292271882500 a + 748669862250 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1748 a - 4480\) , \( -55680 a + 142624\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1748a-4480\right){x}-55680a+142624$ |
| 512.3-i2 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.383506909$ |
$7.665573506$ |
2.852025313 |
\( -20500 a + 54000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 3 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+5\right){x}$ |
| 512.3-i3 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.767013818$ |
$15.33114701$ |
2.852025313 |
\( 2000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-20\right){x}$ |
| 512.3-i4 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{20} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.383506909$ |
$15.33114701$ |
2.852025313 |
\( 20500 a + 33500 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -18 a - 27\) , \( 45 a + 70\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-18a-27\right){x}+45a+70$ |
| 512.3-i5 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.534027637$ |
$7.665573506$ |
2.852025313 |
\( 1098500 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 108 a - 280\) , \( -800 a + 2048\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(108a-280\right){x}-800a+2048$ |
| 512.3-i6 |
512.3-i |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( - 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.068055274$ |
$1.916393376$ |
2.852025313 |
\( 292271882500 a + 456397979750 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 68 a - 240\) , \( -1280 a + 3104\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(68a-240\right){x}-1280a+3104$ |
| 512.3-j1 |
512.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{23} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.490524087$ |
$5.663714500$ |
2.695238627 |
\( 184 a + 560 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -28 a + 76\) , \( 288 a - 736\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+76\right){x}+288a-736$ |
| 512.3-j2 |
512.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.981048174$ |
$11.32742900$ |
2.695238627 |
\( -1092 a + 5588 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 4\) , \( -a - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-4\right){x}-a-4$ |
| 512.3-j3 |
512.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.962096349$ |
$5.663714500$ |
2.695238627 |
\( -10297338 a + 26411786 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 44\) , \( 55 a - 36\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-44\right){x}+55a-36$ |
| 512.3-j4 |
512.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.3 |
\( 2^{9} \) |
\( 2^{17} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.962096349$ |
$11.32742900$ |
2.695238627 |
\( 910322 a + 1430310 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 28 a - 72\) , \( -114 a + 292\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(28a-72\right){x}-114a+292$ |
*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.
