| 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 |
| 1800.2-a1 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{16} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.760464508$ |
$0.765787510$ |
3.294292960 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -20\) , \( 300\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-20{x}+300$ |
| 1800.2-a2 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{2} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.380232254$ |
$1.531575020$ |
3.294292960 |
\( \frac{54607676}{32805} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 20\) , \( -10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+20{x}-10$ |
| 1800.2-a3 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.760464508$ |
$3.063150040$ |
3.294292960 |
\( \frac{3631696}{2025} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-5{x}$ |
| 1800.2-a4 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.380232254$ |
$1.531575020$ |
3.294292960 |
\( \frac{868327204}{5625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -50\) , \( 144\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-50{x}+144$ |
| 1800.2-a5 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.520929017$ |
$3.063150040$ |
3.294292960 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-15{x}+18$ |
| 1800.2-a6 |
1800.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.760464508$ |
$0.765787510$ |
3.294292960 |
\( \frac{1770025017602}{75} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -800\) , \( 8844\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-800{x}+8844$ |
| 1800.2-b1 |
1800.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.963173771$ |
2.461853696 |
\( \frac{21296}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}$ |
| 1800.2-b2 |
1800.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.481586885$ |
2.461853696 |
\( \frac{470596}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-4{x}+2$ |
| 1800.2-b3 |
1800.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{8} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.740793442$ |
2.461853696 |
\( \frac{136835858}{1875} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -34\) , \( -70\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-34{x}-70$ |
| 1800.2-b4 |
1800.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.740793442$ |
2.461853696 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -54\) , \( 162\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-54{x}+162$ |
*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.
