| 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 |
| 2000.2-a1 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{10} \cdot 5^{16} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.670124748$ |
1.340249496 |
\( -\frac{35999730234}{390625} a - \frac{51700389912}{390625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 263 i + 9\) , \( -1092 i - 1365\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(263i+9\right){x}-1092i-1365$ |
| 2000.2-a2 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{10} \cdot 5^{16} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.670124748$ |
1.340249496 |
\( \frac{35999730234}{390625} a - \frac{51700389912}{390625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 82 i + 249\) , \( 1585 i - 810\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(82i+249\right){x}+1585i-810$ |
| 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 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 12 i + 9\) , \( 51 i + 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(12i+9\right){x}+51i+2$ |
| 2000.2-a4 |
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 |
\( -\frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -48 i + 339\) , \( 251 i - 2348\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-48i+339\right){x}+251i-2348$ |
| 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 |
\( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 313 i - 141\) , \( 688 i - 2405\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(313i-141\right){x}+688i-2405$ |
| 2000.2-a6 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.680498993$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -7 i - 6\) , \( -11 i + 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-7i-6\right){x}-11i+2$ |
| 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 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 i + 6\) , \( 2 i - 11\bigr] \) |
${y}^2={x}^{3}+\left(8i+6\right){x}+2i-11$ |
| 2000.2-a8 |
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 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.340249496$ |
1.340249496 |
\( \frac{132304644}{5} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -107 i - 81\) , \( -626 i - 53\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-107i-81\right){x}-626i-53$ |
| 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 |
\( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 1332 i + 3999\) , \( 95335 i - 49560\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(1332i+3999\right){x}+95335i-49560$ |
| 2000.2-a10 |
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 |
\( \frac{15332659200009}{625} a + \frac{5763174879987}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 4213 i + 159\) , \( -70072 i - 80725\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(4213i+159\right){x}-70072i-80725$ |
| 2000.2-b1 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{11} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.436247851$ |
1.436247851 |
\( -\frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 28 i + 53\) , \( -151 i + 109\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(28i+53\right){x}-151i+109$ |
| 2000.2-b2 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{11} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.436247851$ |
1.436247851 |
\( \frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 58 i + 13\) , \( 102 i + 155\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(58i+13\right){x}+102i+155$ |
| 2000.2-b3 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{21} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.436247851 |
\( -\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -162 i + 223\) , \( 1067 i + 1535\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-162i+223\right){x}+1067i+1535$ |
| 2000.2-b4 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{21} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.436247851 |
\( \frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 168 i - 217\) , \( -1540 i + 1061\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(168i-217\right){x}-1540i+1061$ |
| 2000.2-b5 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{18} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.957498567$ |
1.436247851 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -37 i - 27\) , \( -193 i - 35\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-37i-27\right){x}-193i-35$ |
| 2000.2-b6 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 3 i + 3\) , \( 5 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(3i+3\right){x}+5i+1$ |
| 2000.2-b7 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 6 i + 4\) , \( 4 i - 5\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(6i+4\right){x}+4i-5$ |
| 2000.2-b8 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{12} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.957498567$ |
1.436247851 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 166 i + 124\) , \( -108 i + 1111\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(166i+124\right){x}-108i+1111$ |
*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.
