| 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-a5 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{11} \cdot 5^{17} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.749222245$ |
0.749222245 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -61 i - 34\) , \( -48 i + 240\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-61i-34\right){x}-48i+240$ |
| 2000.2-a5 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{11} \cdot 5^{23} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.335062374$ |
1.340249496 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 313 i - 141\) , \( 688 i - 2405\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(313i-141\right){x}+688i-2405$ |
| 2000.3-a5 |
2000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{11} \cdot 5^{23} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.335062374$ |
1.340249496 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 47 i + 339\) , \( 88 i - 2395\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(47i+339\right){x}+88i-2395$ |
| 5000.3-a5 |
5000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5000.3 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{11} \cdot 5^{29} \) |
$1.50283$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.733574011$ |
$0.149844449$ |
2.237821363 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -1501 i - 832\) , \( -4260 i + 27000\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-1501i-832\right){x}-4260i+27000$ |
| 6400.2-a5 |
6400.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{23} \cdot 5^{17} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.888821352$ |
$0.374611122$ |
2.164369220 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -240 i - 133\) , \( 246 i - 1680\bigr] \) |
${y}^2={x}^{3}+\left(-240i-133\right){x}+246i-1680$ |
| 16200.2-a5 |
16200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{11} \cdot 3^{12} \cdot 5^{17} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.735045170$ |
$0.249740748$ |
2.732208912 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -540 i - 300\) , \( -980 i + 5940\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-540i-300\right){x}-980i+5940$ |
| 25600.2-j5 |
25600.2-j |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{29} \cdot 5^{17} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.264890065$ |
2.119120521 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -266 i + 480\) , \( -3852 i + 2868\bigr] \) |
${y}^2={x}^{3}+\left(-266i+480\right){x}-3852i+2868$ |
| 25600.2-p5 |
25600.2-p |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{29} \cdot 5^{17} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.264890065$ |
2.119120521 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 266 i - 480\) , \( -2868 i - 3852\bigr] \) |
${y}^2={x}^{3}+\left(266i-480\right){x}-2868i-3852$ |
| 32000.2-l5 |
32000.2-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{23} \cdot 5^{23} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.167531187$ |
2.680498993 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1252 i - 561\) , \( -6066 i + 17988\bigr] \) |
${y}^2={x}^{3}+\left(1252i-561\right){x}-6066i+17988$ |
| 32000.3-l5 |
32000.3-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{23} \cdot 5^{23} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.167531187$ |
2.680498993 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 188 i + 1359\) , \( -654 i - 18972\bigr] \) |
${y}^2={x}^{3}+\left(188i+1359\right){x}-654i-18972$ |
| 57800.4-e5 |
57800.4-e |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.4 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 5^{17} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.181713085$ |
2.907409369 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1166 i + 18\) , \( -12356 i + 7688\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(1166i+18\right){x}-12356i+7688$ |
| 57800.6-d5 |
57800.6-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 5^{17} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.181713085$ |
2.907409369 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 634 i + 978\) , \( 9964 i + 11152\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(634i+978\right){x}+9964i+11152$ |
| 67600.4-d5 |
67600.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{17} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.258491824$ |
$0.207796863$ |
3.754460134 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 99 i - 887\) , \( 8940 i + 3255\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(99i-887\right){x}+8940i+3255$ |
| 67600.6-f5 |
67600.6-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{17} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.564622956$ |
$0.207796863$ |
3.754460134 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -700 i + 553\) , \( 10213 i - 126\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-700i+553\right){x}+10213i-126$ |
*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.
