| 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-a3 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a\) , \( a\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+2a{x}+a$ |
| 16.4-a3 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{10} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -9 a - 15\) , \( -6 a - 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9a-15\right){x}-6a-10$ |
| 64.7-a3 |
64.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{16} \) |
$1.04210$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.04342268$ |
1.457846637 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3 a - 5\) , \( -2 a - 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3a-5\right){x}-2a-3$ |
| 64.7-b3 |
64.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.7 |
\( 2^{6} \) |
\( 2^{16} \) |
$1.04210$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.493335081$ |
$16.51961138$ |
0.988296755 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 5 a - 13\) , \( 16 a - 41\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-13\right){x}+16a-41$ |
| 128.2-b3 |
128.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.2 |
\( 2^{7} \) |
\( 2^{22} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.68112923$ |
1.416544989 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 7\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-7\right){x}+2a-6$ |
| 256.1-f3 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.269899646$ |
$17.00126722$ |
2.225815404 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a - 36\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a-36\right){x}$ |
| 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-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 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 64 a - 160\) , \( -368 a + 944\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(64a-160\right){x}-368a+944$ |
| 648.4-d3 |
648.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.4 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$1.85890$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.680814550$ |
$11.33417814$ |
1.871519699 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a - 12\) , \( -4 a + 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-12\right){x}-4a+12$ |
*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.
