| 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 |
| 15842.2-a1 |
15842.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{15} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.830797459$ |
1.830797459 |
\( -\frac{5888771351}{22784} a + \frac{10644029209}{22784} \) |
\( \bigl[i\) , \( 0\) , \( 1\) , \( -43 i + 4\) , \( -61 i + 85\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(-43i+4\right){x}-61i+85$ |
| 15842.2-b1 |
15842.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{28} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.384968297$ |
$1.204226331$ |
2.872041624 |
\( \frac{9759185353}{1458176} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -44\) , \( -80\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-44{x}-80$ |
| 15842.2-b2 |
15842.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{14} \cdot 89^{4} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.192484148$ |
$0.602113165$ |
2.872041624 |
\( \frac{35471840526793}{1013888} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -684\) , \( -6608\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-684{x}-6608$ |
| 15842.2-c1 |
15842.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{15} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.830797459$ |
1.830797459 |
\( \frac{5888771351}{22784} a + \frac{10644029209}{22784} \) |
\( \bigl[i\) , \( 0\) , \( 1\) , \( 42 i + 4\) , \( 61 i + 85\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(42i+4\right){x}+61i+85$ |
| 15842.2-d1 |
15842.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{18} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.054763262$ |
$2.346211691$ |
4.625503460 |
\( \frac{688985}{45568} a + \frac{35019}{5696} \) |
\( \bigl[1\) , \( -i - 1\) , \( 0\) , \( 2 i + 1\) , \( -8 i - 7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(2i+1\right){x}-8i-7$ |
| 15842.2-e1 |
15842.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{18} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.054763262$ |
$2.346211691$ |
4.625503460 |
\( -\frac{688985}{45568} a + \frac{35019}{5696} \) |
\( \bigl[i\) , \( -i + 1\) , \( 0\) , \( -2 i + 1\) , \( -8 i + 7\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2i+1\right){x}-8i+7$ |
| 15842.2-f1 |
15842.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{8} \cdot 89^{6} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.551982120$ |
4.415856963 |
\( -\frac{18806241149857}{11279504} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -554\) , \( 5068\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-554{x}+5068$ |
| 15842.2-f2 |
15842.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15842.2 |
\( 2 \cdot 89^{2} \) |
\( 2^{24} \cdot 89^{2} \) |
$2.00503$ |
$(a+1), (-5a+8), (-8a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.655946361$ |
4.415856963 |
\( \frac{23639903}{364544} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 6\) , \( 28\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+6{x}+28$ |
*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.
