| 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-a7 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.993777963$ |
0.749222245 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^{3}-2{x}+1$ |
| 2000.2-a7 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.680498993$ |
1.340249496 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 i + 6\) , \( 2 i - 11\bigr] \) |
${y}^2={x}^{3}+\left(8i+6\right){x}+2i-11$ |
| 2000.3-a7 |
2000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.680498993$ |
1.340249496 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 i + 6\) , \( -2 i - 11\bigr] \) |
${y}^2={x}^{3}+\left(-8i+6\right){x}-2i-11$ |
| 5000.3-a7 |
5000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5000.3 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.50283$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.233348375$ |
$1.198755592$ |
2.237821363 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \) |
${y}^2={x}^{3}-50{x}+125$ |
| 6400.2-a7 |
6400.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.722205338$ |
$5.993777963$ |
2.164369220 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -i\bigr] \) |
${y}^2={x}^{3}+2{x}-i$ |
| 16200.2-a7 |
16200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.170940323$ |
$1.997925987$ |
2.732208912 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18\) , \( -27\bigr] \) |
${y}^2={x}^{3}-18{x}-27$ |
| 25600.2-j7 |
25600.2-j |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.238241043$ |
2.119120521 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 i\) , \( -2 i - 2\bigr] \) |
${y}^2={x}^{3}+4i{x}-2i-2$ |
| 25600.2-p7 |
25600.2-p |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.238241043$ |
2.119120521 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 i\) , \( 2 i - 2\bigr] \) |
${y}^2={x}^{3}-4i{x}+2i-2$ |
| 32000.2-l7 |
32000.2-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.680498993$ |
2.680498993 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 i - 6\) , \( -11 i - 2\bigr] \) |
${y}^2={x}^{3}+\left(-8i-6\right){x}-11i-2$ |
| 32000.3-l7 |
32000.3-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.680498993$ |
2.680498993 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 i - 6\) , \( 11 i - 2\bigr] \) |
${y}^2={x}^{3}+\left(8i-6\right){x}+11i-2$ |
| 57800.4-e7 |
57800.4-e |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.4 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.453704684$ |
2.907409369 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 i + 30\) , \( 52 i - 47\bigr] \) |
${y}^2={x}^{3}+\left(16i+30\right){x}+52i-47$ |
| 57800.6-d7 |
57800.6-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.453704684$ |
2.907409369 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 i + 30\) , \( -52 i - 47\bigr] \) |
${y}^2={x}^{3}+\left(-16i+30\right){x}-52i-47$ |
| 67600.4-d7 |
67600.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.258491824$ |
$1.662374906$ |
3.754460134 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 i - 10\) , \( -46 i - 9\bigr] \) |
${y}^2={x}^{3}+\left(24i-10\right){x}-46i-9$ |
| 67600.6-f7 |
67600.6-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.258491824$ |
$1.662374906$ |
3.754460134 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 i - 10\) , \( -46 i + 9\bigr] \) |
${y}^2={x}^{3}+\left(-24i-10\right){x}-46i+9$ |
*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.
