| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.070288814$ |
$16.29302268$ |
4.507529569 |
\( 128 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 80 a + 304\) , \( 2764 a + 10340\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(80a+304\right){x}+2764a+10340$ |
| 256.1-a2 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.035144407$ |
$32.58604536$ |
4.507529569 |
\( 10976 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}+2$ |
| 256.1-b1 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.816032520$ |
$35.89270325$ |
4.355176705 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a - 20\) , \( -26 a + 98\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a-20\right){x}-26a+98$ |
| 256.1-b2 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.632065040$ |
$17.94635162$ |
4.355176705 |
\( 8000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 20\) , \( -26 a - 98\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-20\right){x}-26a-98$ |
| 256.1-c1 |
256.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.870387548$ |
$7.547952572$ |
2.895180776 |
\( 128 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}-1$ |
| 256.1-c2 |
256.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.435193774$ |
$15.09590514$ |
2.895180776 |
\( 10976 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 280 a - 1043\) , \( 4877 a - 18250\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(280a-1043\right){x}+4877a-18250$ |
| 256.1-d1 |
256.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.67481$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$7.547952572$ |
4.034550356 |
\( 128 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 80 a + 304\) , \( -2764 a - 10340\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(80a+304\right){x}-2764a-10340$ |
| 256.1-d2 |
256.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$2.67481$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$15.09590514$ |
4.034550356 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}-2$ |
| 256.1-e1 |
256.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.816032520$ |
$35.89270325$ |
4.355176705 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 20\) , \( 26 a + 98\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-20\right){x}+26a+98$ |
| 256.1-e2 |
256.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.67481$ |
$(-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.632065040$ |
$17.94635162$ |
4.355176705 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a - 20\) , \( 26 a - 98\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-20\right){x}+26a-98$ |
| 256.1-f1 |
256.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.67481$ |
$(-a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.499403231$ |
$16.29302268$ |
4.349296229 |
\( 128 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}+1$ |
| 256.1-f2 |
256.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{14} \) |
$2.67481$ |
$(-a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.499403231$ |
$32.58604536$ |
4.349296229 |
\( 10976 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 280 a - 1043\) , \( -4877 a + 18250\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(280a-1043\right){x}-4877a+18250$ |
*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.
