| 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 |
| 256.1-a1 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632943382$ |
$7.547952572$ |
2.515907494 |
\( 128 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a + 35\) , \( -131 a - 321\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a+35\right){x}-131a-321$ |
| 256.1-a2 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.816471691$ |
$15.09590514$ |
2.515907494 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}-2$ |
| 256.1-b1 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.432331164$ |
$16.29302268$ |
1.437846696 |
\( 128 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}+1$ |
| 256.1-b2 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.216165582$ |
$32.58604536$ |
1.437846696 |
\( 10976 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 46 a - 112\) , \( -196 a + 480\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-112\right){x}-196a+480$ |
| 256.1-c1 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.579744927$ |
$10.21623143$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-a-3$ |
| 256.1-c2 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.859914975$ |
$30.64869430$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}-a+3$ |
| 256.1-c3 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.289872463$ |
$10.21623143$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 23\) , \( -35 a - 86\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-23\right){x}-35a-86$ |
| 256.1-c4 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.429957487$ |
$30.64869430$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 23\) , \( -35 a + 86\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-23\right){x}-35a+86$ |
| 256.1-d1 |
256.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$27.50074327$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-5\right){x}$ |
| 256.1-d2 |
256.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+5\right){x}$ |
| 256.1-e1 |
256.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$27.50074327$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-5\right){x}$ |
| 256.1-e2 |
256.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+5\right){x}$ |
| 256.1-f1 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.579744927$ |
$10.21623143$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+a-3$ |
| 256.1-f2 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.859914975$ |
$30.64869430$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a + 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}+a+3$ |
| 256.1-f3 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.429957487$ |
$30.64869430$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 23\) , \( 35 a + 86\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-23\right){x}+35a+86$ |
| 256.1-f4 |
256.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.289872463$ |
$10.21623143$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 23\) , \( 35 a - 86\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-23\right){x}+35a-86$ |
| 256.1-g1 |
256.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$16.29302268$ |
3.325799328 |
\( 128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a + 35\) , \( 131 a + 321\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a+35\right){x}+131a+321$ |
| 256.1-g2 |
256.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$32.58604536$ |
3.325799328 |
\( 10976 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}+2$ |
| 256.1-h1 |
256.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.547952572$ |
1.540719367 |
\( 128 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}-1$ |
| 256.1-h2 |
256.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$1.75107$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.09590514$ |
1.540719367 |
\( 10976 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 46 a - 112\) , \( 196 a - 480\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(46a-112\right){x}+196a-480$ |
*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.
