| 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 |
| 2304.2-b2 |
2304.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{15} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.027424501$ |
1.452997663 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 50 a + 14\) , \( 72 a + 198\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(50a+14\right){x}+72a+198$ |
| 2304.2-g2 |
2304.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{15} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.067922392$ |
$1.027424501$ |
3.552878774 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 50 a + 14\) , \( -72 a - 198\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(50a+14\right){x}-72a-198$ |
| 3456.2-b2 |
3456.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{21} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.186367624$ |
0.838888592 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -6 a - 54\) , \( -47 a - 136\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-6a-54\right){x}-47a-136$ |
| 3456.2-g2 |
3456.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{21} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.186367624$ |
2.516665776 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6 a - 54\) , \( 47 a + 136\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-54\right){x}+47a+136$ |
| 3456.3-a2 |
3456.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{21} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.186367624$ |
0.838888592 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -19 a + 46\) , \( -93 a - 125\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-19a+46\right){x}-93a-125$ |
| 3456.3-h2 |
3456.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{21} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.186367624$ |
2.516665776 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -19 a + 46\) , \( 93 a + 125\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a+46\right){x}+93a+125$ |
| 9216.2-n2 |
9216.2-n |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{25} \cdot 3^{15} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.326932873$ |
$0.726498831$ |
4.089970036 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -100 a - 28\) , \( 396 a - 288\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-100a-28\right){x}+396a-288$ |
| 9216.2-p2 |
9216.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{25} \cdot 3^{15} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.326932873$ |
$0.726498831$ |
4.089970036 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -100 a - 28\) , \( -396 a + 288\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-100a-28\right){x}-396a+288$ |
| 20736.3-d2 |
20736.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{27} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.342474833$ |
1.937330218 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 450 a + 123\) , \( -2394 a - 5470\bigr] \) |
${y}^2={x}^{3}+\left(450a+123\right){x}-2394a-5470$ |
| 20736.3-x2 |
20736.3-x |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{27} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.655143300$ |
$0.342474833$ |
5.143889349 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 450 a + 123\) , \( 2394 a + 5470\bigr] \) |
${y}^2={x}^{3}+\left(450a+123\right){x}+2394a+5470$ |
| 27648.2-u2 |
27648.2-u |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.775452707$ |
$0.419444296$ |
3.679887945 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 46 a + 427\) , \( -2223 a + 1075\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(46a+427\right){x}-2223a+1075$ |
| 27648.2-ba2 |
27648.2-ba |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.419444296$ |
3.559102873 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 46 a + 427\) , \( 2223 a - 1075\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(46a+427\right){x}+2223a-1075$ |
| 27648.3-g2 |
27648.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.101810829$ |
$0.419444296$ |
3.679887945 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 154 a - 373\) , \( 1847 a - 2605\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(154a-373\right){x}+1847a-2605$ |
| 27648.3-bq2 |
27648.3-bq |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{21} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.419444296$ |
3.559102873 |
\( \frac{5577343220}{531441} a - \frac{1362907864}{531441} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 154 a - 373\) , \( -1847 a + 2605\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(154a-373\right){x}-1847a+2605$ |
*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.
