| 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 |
| 16.2-a1 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$93.59270615$ |
1.316250266 |
\( 95505 a^{2} - 288104 a + 153504 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 37178 a^{2} - 19692 a - 157999\) , \( 5562481 a^{2} - 2944283 a - 23635709\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(37178a^{2}-19692a-157999\right){x}+5562481a^{2}-2944283a-23635709$ |
| 16.2-a2 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{11} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.39817653$ |
1.316250266 |
\( 103101005876 a^{2} - 290083733531 a + 113696309796 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6407 a^{2} + 3208 a + 26891\) , \( 17854891 a^{2} - 9448825 a - 75864197\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6407a^{2}+3208a+26891\right){x}+17854891a^{2}-9448825a-75864197$ |
| 16.2-a3 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.39817653$ |
1.316250266 |
\( -343127540 a^{2} + 181623451 a + 1457997356 \) |
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( 5718326614 a^{2} - 3026804944 a - 24297973164\) , \( 344200023976745 a^{2} - 182190779570766 a - 1462554275103174\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(5718326614a^{2}-3026804944a-24297973164\right){x}+344200023976745a^{2}-182190779570766a-1462554275103174$ |
| 16.2-a4 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$93.59270615$ |
1.316250266 |
\( -97 a^{2} - 314 a + 1270 \) |
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( -710 a^{2} + 377 a + 3018\) , \( -11698 a^{2} + 6191 a + 49704\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-710a^{2}+377a+3018\right){x}-11698a^{2}+6191a+49704$ |
| 16.2-a5 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{11} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$46.79635307$ |
1.316250266 |
\( -2320978186626 a^{2} + 1226457049213 a + 9867024470514 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 108 a^{2} - 82 a - 507\) , \( -1006 a^{2} + 425 a + 4083\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(108a^{2}-82a-507\right){x}-1006a^{2}+425a+4083$ |
| 16.2-a6 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$93.59270615$ |
1.316250266 |
\( 155385857 a^{2} + 210010108 a - 130120956 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -7 a^{2} - 22 a - 17\) , \( -65 a^{2} - 71 a + 85\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-7a^{2}-22a-17\right){x}-65a^{2}-71a+85$ |
| 16.2-a7 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$187.1854123$ |
1.316250266 |
\( 4165 a^{2} + 5890 a - 1058 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -2 a^{2} - 2 a + 3\) , \( -2 a^{2} - 3 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{2}-2a+3\right){x}-2a^{2}-3a+1$ |
| 16.2-a8 |
16.2-a |
$8$ |
$16$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.52156$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$11.69908826$ |
1.316250266 |
\( 189657446701367682 a^{2} + 254695362995847043 a - 161898141766190114 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -202 a^{2} - 282 a + 153\) , \( -3296 a^{2} - 4399 a + 2863\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-202a^{2}-282a+153\right){x}-3296a^{2}-4399a+2863$ |
*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.
