| 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 |
| 512.1-a4 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$0.85013$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.920761445$ |
0.980190361 |
\( 10976 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 4 i\) , \( -4 i - 4\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+4i{x}-4i-4$ |
| 512.1-b4 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$0.85013$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.920761445$ |
0.980190361 |
\( 10976 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -4 i\) , \( -4 i + 4\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-4i{x}-4i+4$ |
| 1024.1-a4 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.01098$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.216165582$ |
$5.544794010$ |
1.198593625 |
\( 10976 \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 2\) , \( 2 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+2{x}+2i$ |
| 1024.1-b4 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.01098$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.544794010$ |
1.386198502 |
\( 10976 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}+2$ |
| 12800.1-a4 |
12800.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.1 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.381642496$ |
$1.753417822$ |
2.676715022 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14 i + 19\) , \( 18 i + 39\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-14i+19\right){x}+18i+39$ |
| 12800.1-c4 |
12800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.1 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.753417822$ |
1.753417822 |
\( 10976 \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 14 i - 19\) , \( -39 i + 18\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(14i-19\right){x}-39i+18$ |
| 12800.3-a4 |
12800.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.3 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.381642496$ |
$1.753417822$ |
2.676715022 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 14 i + 19\) , \( -18 i + 39\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(14i+19\right){x}-18i+39$ |
| 12800.3-c4 |
12800.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.3 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.753417822$ |
1.753417822 |
\( 10976 \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -14 i - 19\) , \( 39 i + 18\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-14i-19\right){x}+39i+18$ |
| 25600.1-c4 |
25600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.312629616$ |
$2.479707265$ |
3.254937196 |
\( 10976 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 10 i + 7\) , \( -3 i - 13\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(10i+7\right){x}-3i-13$ |
| 25600.1-l4 |
25600.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.479707265$ |
2.479707265 |
\( 10976 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -10 i - 7\) , \( 13 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-10i-7\right){x}+13i-3$ |
| 25600.3-c4 |
25600.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.312629616$ |
$2.479707265$ |
3.254937196 |
\( 10976 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -10 i + 7\) , \( -3 i + 13\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-10i+7\right){x}-3i+13$ |
| 25600.3-l4 |
25600.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.479707265$ |
2.479707265 |
\( 10976 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 10 i - 7\) , \( 13 i + 3\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(10i-7\right){x}+13i+3$ |
| 41472.1-c4 |
41472.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41472.1 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{12} \) |
$2.55039$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.753077976$ |
$1.306920481$ |
3.936852128 |
\( 10976 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -42 i\) , \( 68 i - 68\bigr] \) |
${y}^2={x}^{3}-42i{x}+68i-68$ |
| 41472.1-g4 |
41472.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41472.1 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{12} \) |
$2.55039$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.753077976$ |
$1.306920481$ |
3.936852128 |
\( 10976 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 42 i\) , \( -68 i - 68\bigr] \) |
${y}^2={x}^{3}+42i{x}-68i-68$ |
| 82944.1-e4 |
82944.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.03295$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.848264670$ |
1.848264670 |
\( 10976 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 34\bigr] \) |
${y}^2={x}^{3}-21{x}+34$ |
| 82944.1-q4 |
82944.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{12} \) |
$3.03295$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.816471691$ |
$1.848264670$ |
6.036223124 |
\( 10976 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21\) , \( 34 i\bigr] \) |
${y}^2={x}^{3}+21{x}+34i$ |
| 86528.1-a4 |
86528.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.1 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.087423571$ |
1.087423571 |
\( 10976 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -24 i - 56\) , \( -104 i - 112\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-24i-56\right){x}-104i-112$ |
| 86528.1-b4 |
86528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.1 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.451713319$ |
$1.087423571$ |
6.314509131 |
\( 10976 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 24 i + 56\) , \( 112 i - 104\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(24i+56\right){x}+112i-104$ |
| 86528.3-a4 |
86528.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.3 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.087423571$ |
1.087423571 |
\( 10976 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 24 i - 56\) , \( 104 i - 112\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(24i-56\right){x}+104i-112$ |
| 86528.3-b4 |
86528.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.3 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.451713319$ |
$1.087423571$ |
6.314509131 |
\( 10976 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -24 i + 56\) , \( -112 i - 104\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-24i+56\right){x}-112i-104$ |
*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.
