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 |
588.2-a4 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.342545916$ |
0.791075908 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
12348.2-b4 |
12348.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{14} \cdot 7^{22} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.074749647$ |
1.381015326 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 13710 a + 8226\) , \( -638437 a + 1167672\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13710a+8226\right){x}-638437a+1167672$ |
12348.3-b4 |
12348.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{14} \cdot 7^{22} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.074749647$ |
1.381015326 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -13711 a + 21937\) , \( 638437 a + 529235\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-13711a+21937\right){x}+638437a+529235$ |
28812.3-f4 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{28} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.106462011$ |
$0.048935130$ |
4.001350588 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44787 a + 44787\) , \( 3609423\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-44787a+44787\right){x}+3609423$ |
37632.2-r4 |
37632.2-r |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{8} \cdot 7^{16} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{11} \) |
$1$ |
$0.085636479$ |
3.164303633 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14624\) , \( 669300\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-14624{x}+669300$ |
99372.4-g4 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7311 a + 13710\) , \( -380137 a - 170928\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7311a+13710\right){x}-380137a-170928$ |
99372.6-h4 |
99372.6-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.6 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13710 a + 7313\) , \( 386535 a - 564775\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13710a+7313\right){x}+386535a-564775$ |
112896.2-k4 |
112896.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{14} \cdot 7^{16} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.049442244$ |
0.913455777 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 43873\) , \( 4059673 a - 2007900\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+43873\right){x}+4059673a-2007900$ |
112896.2-u4 |
112896.2-u |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{14} \cdot 7^{16} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.049442244$ |
0.913455777 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -43872 a\) , \( -4015800 a + 2007900\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-43872a{x}-4015800a+2007900$ |
*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.