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 |
3087.2-a1 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{7} \cdot 7^{26} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.094060304$ |
1.737783746 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 3474 a + 6465\) , \( -321486 a + 306732\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(3474a+6465\right){x}-321486a+306732$ |
3087.2-a2 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{7} \cdot 7^{26} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.094060304$ |
1.737783746 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 654 a - 9045\) , \( -19194 a + 323526\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(654a-9045\right){x}-19194a+323526$ |
3087.2-a3 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{22} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -816 a + 510\) , \( -13020 a + 24087\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-816a+510\right){x}-13020a+24087$ |
3087.2-a4 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{10} \cdot 7^{8} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.504964870$ |
1.737783746 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 24 a - 15\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(24a-15\right){x}$ |
3087.2-a5 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{14} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.752482435$ |
1.737783746 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -96 a + 60\) , \( -60 a + 111\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-96a+60\right){x}-60a+111$ |
3087.2-a6 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{22} \cdot 7^{8} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -936 a + 585\) , \( 5400 a - 9990\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-936a+585\right){x}+5400a-9990$ |
3087.2-a7 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{10} \cdot 7^{14} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -1176 a + 735\) , \( -8160 a + 15096\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-1176a+735\right){x}-8160a+15096$ |
3087.2-a8 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -18816 a + 11760\) , \( -510900 a + 945165\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-18816a+11760\right){x}-510900a+945165$ |
*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.