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 |
8.4-a2 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a + 13\) , \( 33 a - 86\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-6a+13\right){x}+33a-86$ |
16.4-a2 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$ |
64.7-a2 |
64.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 3\) , \( -2 a + 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}-2a+5$ |
64.7-b2 |
64.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{17} \) |
$1.04210$ |
$(-a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.986670162$ |
$8.259805693$ |
0.988296755 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 5 a + 8\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(5a+8\right){x}$ |
128.2-b2 |
128.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.2 |
\( 2^{7} \) |
\( 2^{23} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.840564617$ |
1.416544989 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 37 a + 60\) , \( -38 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(37a+60\right){x}-38a-60$ |
256.1-f2 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.134949823$ |
$8.500633610$ |
2.225815404 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$ |
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-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 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7 a + 12\) , \( 7 a + 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(7a+12\right){x}+7a+12$ |
648.4-d2 |
648.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.4 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{12} \) |
$1.85890$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.361629101$ |
$5.667089073$ |
1.871519699 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -51 a + 132\) , \( -948 a + 2428\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-51a+132\right){x}-948a+2428$ |
*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.