| 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-a3 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 12 a - 37\) , \( 46 a - 121\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(12a-37\right){x}+46a-121$ |
| 16.5-a3 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+3\right){x}$ |
| 64.6-a3 |
64.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{14} \) |
$1.04210$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.04342268$ |
1.457846637 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -34 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-8\right){x}-34a-53$ |
| 64.6-b3 |
64.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{14} \) |
$1.04210$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.246667540$ |
$33.03922277$ |
0.988296755 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 3 a - 13\) , \( -9 a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(3a-13\right){x}-9a+20$ |
| 128.1-b3 |
128.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( 2^{20} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$23.36225846$ |
1.416544989 |
\( -24225 a + 68453 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 33 a - 84\) , \( -178 a + 456\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(33a-84\right){x}-178a+456$ |
| 256.1-e3 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -24225 a + 68453 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4a-8\right){x}-8a-12$ |
| 512.4-e3 |
512.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( -24225 a + 68453 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -94 a - 145\) , \( -655 a - 1023\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-94a-145\right){x}-655a-1023$ |
| 512.4-h3 |
512.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{26} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.530294222$ |
1.583828990 |
\( -24225 a + 68453 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 17\) , \( 9 a - 33\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-17\right){x}+9a-33$ |
| 648.3-d3 |
648.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.85890$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.340407275$ |
$11.33417814$ |
1.871519699 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 123 a - 316\) , \( -1017 a + 2604\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(123a-316\right){x}-1017a+2604$ |
*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.
