| 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 |
| 1800.1-a1 |
1800.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.151320779$ |
$22.50857439$ |
2.408416311 |
\( -\frac{22335584}{75} a + \frac{10601168}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 7 a - 11\) , \( -8 a + 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-11\right){x}-8a+11$ |
| 1800.1-a2 |
1800.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.075660389$ |
$22.50857439$ |
2.408416311 |
\( \frac{161792}{15} a + \frac{772096}{45} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 4\) , \( -2 a + 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-4\right){x}-2a+3$ |
| 1800.1-b1 |
1800.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.223522115$ |
$8.143100067$ |
2.574099130 |
\( -\frac{865504}{675} a - \frac{3363568}{2025} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -3 a\) , \( 4 a - 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}-3a{x}+4a-2$ |
| 1800.1-b2 |
1800.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.111761057$ |
$16.28620013$ |
2.574099130 |
\( \frac{276826112}{45} a + \frac{130648064}{15} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -13\) , \( 9 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-13{x}+9a-2$ |
| 1800.1-c1 |
1800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.39841016$ |
2.191749975 |
\( \frac{21296}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}$ |
| 1800.1-c2 |
1800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$12.39841016$ |
2.191749975 |
\( \frac{470596}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-4{x}-2$ |
| 1800.1-c3 |
1800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{8} \) |
$1.64627$ |
$(a), (3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$12.39841016$ |
2.191749975 |
\( \frac{136835858}{1875} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -34\) , \( 70\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-34{x}+70$ |
| 1800.1-c4 |
1800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.099602540$ |
2.191749975 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -54\) , \( -162\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-54{x}-162$ |
| 1800.1-d1 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{16} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.146228852$ |
$0.805807860$ |
2.612449050 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -20\) , \( -300\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-20{x}-300$ |
| 1800.1-d2 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.573114426$ |
$3.223231443$ |
2.612449050 |
\( \frac{54607676}{32805} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 20\) , \( 10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+20{x}+10$ |
| 1800.1-d3 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.146228852$ |
$12.89292577$ |
2.612449050 |
\( \frac{3631696}{2025} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-5{x}$ |
| 1800.1-d4 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.573114426$ |
$3.223231443$ |
2.612449050 |
\( \frac{868327204}{5625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -50\) , \( -144\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-50{x}-144$ |
| 1800.1-d5 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.573114426$ |
$25.78585154$ |
2.612449050 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-15{x}+18$ |
| 1800.1-d6 |
1800.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1.146228852$ |
$0.805807860$ |
2.612449050 |
\( \frac{1770025017602}{75} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -800\) , \( -8844\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-800{x}-8844$ |
| 1800.1-e1 |
1800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.223522115$ |
$8.143100067$ |
2.574099130 |
\( \frac{865504}{675} a - \frac{3363568}{2025} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 3 a\) , \( -4 a - 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+3a{x}-4a-2$ |
| 1800.1-e2 |
1800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.111761057$ |
$16.28620013$ |
2.574099130 |
\( -\frac{276826112}{45} a + \frac{130648064}{15} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -13\) , \( -9 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-13{x}-9a-2$ |
| 1800.1-f1 |
1800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.075660389$ |
$22.50857439$ |
2.408416311 |
\( -\frac{161792}{15} a + \frac{772096}{45} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 4\) , \( 2 a + 3\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a-4\right){x}+2a+3$ |
| 1800.1-f2 |
1800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1800.1 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
$1.64627$ |
$(a), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.151320779$ |
$22.50857439$ |
2.408416311 |
\( \frac{22335584}{75} a + \frac{10601168}{25} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -7 a - 11\) , \( 8 a + 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-11\right){x}+8a+11$ |
*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.
