| 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 |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$0.73687$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.518320950$ |
0.828555571 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -38 a - 77\) , \( -268 a - 444\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-38a-77\right){x}-268a-444$ |
| 64.2-a1 |
64.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.2 |
\( 2^{6} \) |
\( - 2^{12} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$6.298617478$ |
1.145729345 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 284 a - 728\) , \( -3599 a + 9219\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(284a-728\right){x}-3599a+9219$ |
| 64.3-a1 |
64.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.3 |
\( 2^{6} \) |
\( - 2^{12} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$6.298617478$ |
1.145729345 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 284 a - 728\) , \( 3599 a - 9219\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(284a-728\right){x}+3599a-9219$ |
| 256.1-d1 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{12} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$26.12924634$ |
1.584318273 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -38 a - 77\) , \( 268 a + 444\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-38a-77\right){x}+268a+444$ |
| 256.4-a1 |
256.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.4 |
\( 2^{8} \) |
\( - 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.453795131$ |
1.620305978 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 41 a - 161\) , \( 369 a - 801\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(41a-161\right){x}+369a-801$ |
| 256.4-d1 |
256.4-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.4 |
\( 2^{8} \) |
\( - 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.491374562$ |
$18.47616728$ |
2.201912694 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -900 a - 1408\) , \( 21952 a + 34280\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-900a-1408\right){x}+21952a+34280$ |
| 256.5-a1 |
256.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.5 |
\( 2^{8} \) |
\( - 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.453795131$ |
1.620305978 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -548 a - 861\) , \( -9901 a - 15454\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-548a-861\right){x}-9901a-15454$ |
| 256.5-d1 |
256.5-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.5 |
\( 2^{8} \) |
\( - 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.245687281$ |
$18.47616728$ |
2.201912694 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 81 a - 241\) , \( -564 a + 1540\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(81a-241\right){x}-564a+1540$ |
*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.
