| 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-a5 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{4} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a - 8\) , \( 2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a-8\right){x}+2a+3$ |
| 16.5-a5 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{4} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9.235230655$ |
0.559968109 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 4\) , \( 5 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}+5a-16$ |
| 64.6-a5 |
64.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( - 2^{10} \) |
$1.04210$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.02171134$ |
1.457846637 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a\) , \( -2 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-2a+1$ |
| 64.6-b5 |
64.6-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.6 |
\( 2^{6} \) |
\( - 2^{10} \) |
$1.04210$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123333770$ |
$33.03922277$ |
0.988296755 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 13 a - 30\) , \( -534 a + 1369\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(13a-30\right){x}-534a+1369$ |
| 128.1-b5 |
128.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( - 2^{16} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.36225846$ |
1.416544989 |
\( 7659605 a + 11960871 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -28 a - 43\) , \( 142 a + 222\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-28a-43\right){x}+142a+222$ |
| 256.1-e5 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( 7659605 a + 11960871 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a - 4\) , \( -22 a + 56\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a-4\right){x}-22a+56$ |
| 512.4-e5 |
512.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.010855670$ |
1.457846637 |
\( 7659605 a + 11960871 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -9 a - 13\) , \( -18 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-13\right){x}-18a-21$ |
| 512.4-h5 |
512.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{22} \) |
$1.75259$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.265147111$ |
1.583828990 |
\( 7659605 a + 11960871 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 19 a - 45\) , \( 972 a - 2491\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(19a-45\right){x}+972a-2491$ |
| 648.3-d5 |
648.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
648.3 |
\( 2^{3} \cdot 3^{4} \) |
\( - 2^{4} \cdot 3^{12} \) |
$1.85890$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.680814550$ |
$5.667089073$ |
1.871519699 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -39 a - 61\) , \( -244 a - 380\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-39a-61\right){x}-244a-380$ |
*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.
