| 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-a3 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.996888981$ |
0.749222245 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -4\) , \( -6 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-4{x}-6i$ |
| 2000.2-a3 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.340249496$ |
1.340249496 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 12 i + 9\) , \( 51 i + 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(12i+9\right){x}+51i+2$ |
| 2000.3-a3 |
2000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.340249496$ |
1.340249496 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -14 i + 9\) , \( 51 i - 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-14i+9\right){x}+51i-2$ |
| 5000.3-a3 |
5000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5000.3 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{20} \) |
$1.50283$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.933393502$ |
$0.599377796$ |
2.237821363 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -82\) , \( -572 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-82{x}-572i$ |
| 6400.2-a3 |
6400.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.722205338$ |
$1.498444490$ |
2.164369220 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -13\) , \( 34 i\bigr] \) |
${y}^2={x}^{3}-13{x}+34i$ |
| 16200.2-a3 |
16200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{8} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.683761292$ |
$0.998962993$ |
2.732208912 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -30\) , \( 100 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-30{x}+100i$ |
| 25600.2-j3 |
25600.2-j |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{8} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.059560260$ |
2.119120521 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -26 i\) , \( 68 i + 68\bigr] \) |
${y}^2={x}^{3}-26i{x}+68i+68$ |
| 25600.2-p3 |
25600.2-p |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{8} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.059560260$ |
2.119120521 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 26 i\) , \( -68 i + 68\bigr] \) |
${y}^2={x}^{3}+26i{x}-68i+68$ |
| 32000.2-l3 |
32000.2-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{14} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.670124748$ |
2.680498993 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 52 i + 39\) , \( 374 i + 68\bigr] \) |
${y}^2={x}^{3}+\left(52i+39\right){x}+374i+68$ |
| 32000.3-l3 |
32000.3-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{14} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.670124748$ |
2.680498993 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -52 i + 39\) , \( -374 i + 68\bigr] \) |
${y}^2={x}^{3}+\left(-52i+39\right){x}-374i+68$ |
| 57800.4-e3 |
57800.4-e |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.4 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.726852342$ |
2.907409369 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 26 i + 48\) , \( 224 i + 208\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(26i+48\right){x}+224i+208$ |
| 57800.6-d3 |
57800.6-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.726852342$ |
2.907409369 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -26 i + 48\) , \( 224 i - 208\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-26i+48\right){x}+224i-208$ |
| 67600.4-d3 |
67600.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.564622956$ |
$0.831187453$ |
3.754460134 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 39 i - 17\) , \( 30 i - 215\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(39i-17\right){x}+30i-215$ |
| 67600.6-f3 |
67600.6-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.564622956$ |
$0.831187453$ |
3.754460134 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -40 i - 17\) , \( -47 i - 176\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-40i-17\right){x}-47i-176$ |
*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.
