| 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 |
| 8.3-a6 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 12\) , \( -29 a - 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-12\right){x}-29a-31$ |
| 16.5-a6 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 127 a - 317\) , \( -1109 a + 2848\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a-317\right){x}-1109a+2848$ |
| 64.6-a6 |
64.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 38 a - 103\) , \( 203 a - 514\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(38a-103\right){x}+203a-514$ |
| 64.6-b6 |
64.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.986670162$ |
$4.129902846$ |
0.988296755 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -90 a - 143\) , \( -779 a - 1218\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-90a-143\right){x}-779a-1218$ |
| 128.1-b6 |
128.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( 2^{23} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.920282308$ |
1.416544989 |
\( 21069823 a + 33751811 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a - 84\) , \( -218 a - 388\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-43a-84\right){x}-218a-388$ |
| 256.1-e6 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539799292$ |
$8.500633610$ |
2.225815404 |
\( 21069823 a + 33751811 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 305 a - 780\) , \( 4096 a - 10492\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(305a-780\right){x}+4096a-10492$ |
| 512.4-e6 |
512.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( 21069823 a + 33751811 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 44 a - 172\) , \( 352 a - 768\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(44a-172\right){x}+352a-768$ |
| 512.4-h6 |
512.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{29} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.06058844$ |
1.583828990 |
\( 21069823 a + 33751811 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -982 a - 1537\) , \( 25287 a + 39489\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-982a-1537\right){x}+25287a+39489$ |
| 648.3-d6 |
648.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{12} \) |
$1.85890$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.361629101$ |
$5.667089073$ |
1.871519699 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -48 a - 145\) , \( 379 a + 340\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-48a-145\right){x}+379a+340$ |
*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.
