| 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-a4 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -14 a - 23\) , \( -47 a - 74\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-14a-23\right){x}-47a-74$ |
| 16.4-a4 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}$ |
| 64.7-a4 |
64.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{14} \) |
$1.04210$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.04342268$ |
1.457846637 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 10 a - 20\) , \( 15 a - 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(10a-20\right){x}+15a-36$ |
| 64.7-b4 |
64.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{14} \) |
$1.04210$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.246667540$ |
$33.03922277$ |
0.988296755 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 8\) , \( 8 a + 12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-5a-8\right){x}+8a+12$ |
| 128.2-b4 |
128.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.2 |
\( 2^{7} \) |
\( 2^{20} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$23.36225846$ |
1.416544989 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -33 a - 51\) , \( 178 a + 278\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-33a-51\right){x}+178a+278$ |
| 256.1-f4 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539799292$ |
$17.00126722$ |
2.225815404 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 12\) , \( 8 a - 20\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a-12\right){x}+8a-20$ |
| 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-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 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 12\) , \( -4 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-12\right){x}-4a-12$ |
| 648.4-d4 |
648.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.4 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.85890$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.340407275$ |
$11.33417814$ |
1.871519699 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -123 a - 192\) , \( 1140 a + 1780\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-123a-192\right){x}+1140a+1780$ |
*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.
