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-a4 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+3\right){x}$ |
16.5-a4 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{10} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$ |
64.6-a4 |
64.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{16} \) |
$1.04210$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$24.04342268$ |
1.457846637 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a - 8\) , \( 2 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-8\right){x}+2a-5$ |
64.6-b4 |
64.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( 2^{16} \) |
$1.04210$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.493335081$ |
$16.51961138$ |
0.988296755 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 8\) , \( -16 a - 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-8\right){x}-16a-25$ |
128.1-b4 |
128.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( 2^{22} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.68112923$ |
1.416544989 |
\( 1995 a + 5021 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 4\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-4\right){x}-2a-4$ |
256.1-e4 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
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 |
\( 1995 a + 5021 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a - 60\) , \( 24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-60\right){x}+24a-60$ |
512.4-e4 |
512.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( 1995 a + 5021 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(4a-12\right){x}$ |
512.4-h4 |
512.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( 2^{28} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$13.06058844$ |
1.583828990 |
\( 1995 a + 5021 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -62 a - 97\) , \( 431 a + 673\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-62a-97\right){x}+431a+673$ |
648.3-d4 |
648.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$1.85890$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.680814550$ |
$11.33417814$ |
1.871519699 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3 a - 10\) , \( a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-3a-10\right){x}+a-2$ |
*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.