| 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 |
| 16384.1-CMh1 |
16384.1-CMh |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.088009945$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2i-2\right){x}$ |
| 16384.1-CMg1 |
16384.1-CMg |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.088009945$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2i-2\right){x}$ |
| 16384.1-CMf1 |
16384.1-CMf |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.088009945$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2i+2\right){x}$ |
| 16384.1-CMe1 |
16384.1-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.088009945$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2i+2\right){x}$ |
| 16384.1-CMd1 |
16384.1-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.781319108$ |
2.890659554 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( i - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}$ |
| 16384.1-CMc1 |
16384.1-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.271805423$ |
$5.781319108$ |
3.142787774 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( i + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}$ |
| 16384.1-CMb1 |
16384.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.271805423$ |
$5.781319108$ |
3.142787774 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -i + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}$ |
| 16384.1-CMa1 |
16384.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.781319108$ |
2.890659554 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -i - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}$ |
| 16384.1-a1 |
16384.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$0.300177438$ |
$5.441902473$ |
3.267072692 |
\( -3008 a - 3328 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -i - 1\) , \( -2 i\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-i-1\right){x}-2i$ |
| 16384.1-a2 |
16384.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$0.300177438$ |
$5.441902473$ |
3.267072692 |
\( 3008 a - 3328 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( i - 1\) , \( -2 i\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(i-1\right){x}-2i$ |
| 16384.1-b1 |
16384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.848006141$ |
1.924003070 |
\( -3008 a - 3328 \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -2 i + 3\) , \( i + 2\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-2i+3\right){x}+i+2$ |
| 16384.1-b2 |
16384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.848006141$ |
1.924003070 |
\( 3008 a - 3328 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 i - 3\) , \( -2 i - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2i-3\right){x}-2i-1$ |
| 16384.1-c1 |
16384.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.848006141$ |
1.924003070 |
\( -3008 a - 3328 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 i - 3\) , \( 2 i - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2i-3\right){x}+2i-1$ |
| 16384.1-c2 |
16384.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.848006141$ |
1.924003070 |
\( 3008 a - 3328 \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 2 i + 3\) , \( i - 2\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(2i+3\right){x}+i-2$ |
| 16384.1-d1 |
16384.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$5.441902473$ |
2.720951236 |
\( -3008 a - 3328 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( i + 1\) , \( -2\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(i+1\right){x}-2$ |
| 16384.1-d2 |
16384.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.02196$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$5.441902473$ |
2.720951236 |
\( 3008 a - 3328 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -i + 1\) , \( -2\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-i+1\right){x}-2$ |
*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.
