| 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 |
| 200.2-a9 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{5} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.749222245$ |
0.749222245 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 480 i - 694\) , \( -7778 i + 5556\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(480i-694\right){x}-7778i+5556$ |
| 2000.2-a9 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{11} \cdot 5^{11} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.335062374$ |
1.340249496 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 1332 i + 3999\) , \( 95335 i - 49560\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(1332i+3999\right){x}+95335i-49560$ |
| 2000.3-a9 |
2000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{11} \cdot 5^{11} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.335062374$ |
1.340249496 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -4214 i + 159\) , \( 70231 i - 76512\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-4214i+159\right){x}+70231i-76512$ |
| 5000.3-a9 |
5000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5000.3 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{11} \cdot 5^{17} \) |
$1.50283$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.733574011$ |
$0.149844449$ |
2.237821363 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 12000 i - 17332\) , \( -937572 i + 718500\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(12000i-17332\right){x}-937572i+718500$ |
| 6400.2-a9 |
6400.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{23} \cdot 5^{5} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.888821352$ |
$0.374611122$ |
2.164369220 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1920 i - 2773\) , \( 59450 i - 46368\bigr] \) |
${y}^2={x}^{3}+\left(1920i-2773\right){x}+59450i-46368$ |
| 16200.2-a9 |
16200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{12} \cdot 5^{5} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.735045170$ |
$0.249740748$ |
2.732208912 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 4320 i - 6240\) , \( 197524 i - 158652\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(4320i-6240\right){x}+197524i-158652$ |
| 25600.2-j9 |
25600.2-j |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{29} \cdot 5^{5} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.264890065$ |
2.119120521 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5546 i - 3840\) , \( 211636 i + 26164\bigr] \) |
${y}^2={x}^{3}+\left(-5546i-3840\right){x}+211636i+26164$ |
| 25600.2-p9 |
25600.2-p |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{29} \cdot 5^{5} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.264890065$ |
2.119120521 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5546 i + 3840\) , \( -26164 i + 211636\bigr] \) |
${y}^2={x}^{3}+\left(5546i+3840\right){x}-26164i+211636$ |
| 32000.2-l9 |
32000.2-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{23} \cdot 5^{11} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.167531187$ |
2.680498993 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5332 i + 15999\) , \( 746686 i - 391148\bigr] \) |
${y}^2={x}^{3}+\left(5332i+15999\right){x}+746686i-391148$ |
| 32000.3-l9 |
32000.3-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{23} \cdot 5^{11} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.167531187$ |
2.680498993 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16852 i + 639\) , \( -561214 i + 628948\bigr] \) |
${y}^2={x}^{3}+\left(-16852i+639\right){x}-561214i+628948$ |
| 57800.4-e9 |
57800.4-e |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.4 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 5^{5} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.181713085$ |
2.907409369 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -1654 i + 14238\) , \( 657780 i + 114840\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-1654i+14238\right){x}+657780i+114840$ |
| 57800.6-d9 |
57800.6-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 5^{5} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.181713085$ |
2.907409369 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -12746 i + 6558\) , \( 51156 i - 652464\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-12746i+6558\right){x}+51156i-652464$ |
| 67600.4-d9 |
67600.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{5} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$0.564622956$ |
$0.207796863$ |
3.754460134 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 10719 i + 2293\) , \( -198588 i - 399361\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(10719i+2293\right){x}-198588i-399361$ |
| 67600.6-f9 |
67600.6-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{5} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.258491824$ |
$0.207796863$ |
3.754460134 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -5920 i - 9227\) , \( -338111 i - 286714\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-5920i-9227\right){x}-338111i-286714$ |
*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.
