| 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 |
| 2.1-c2 |
2.1-c |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$2.71558$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$141.4248935$ |
1.305911907 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( 1\) , \( -16355430935 a^{2} - 24830793973 a + 51959143466\) , \( 2128166401426176 a^{2} + 3230979462595240 a - 6760916529725773\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16355430935a^{2}-24830793973a+51959143466\right){x}+2128166401426176a^{2}+3230979462595240a-6760916529725773$ |
| 16.3-f6 |
16.3-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{13} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$74.06964430$ |
0.341978091 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( 0\) , \( -897 a^{2} - 1369 a + 2861\) , \( 27605 a^{2} + 41911 a - 87698\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-897a^{2}-1369a+2861\right){x}+27605a^{2}+41911a-87698$ |
| 50.2-f6 |
50.2-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( - 2 \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$52.71851719$ |
3.894405722 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} + a - 4\) , \( -2865874952308 a^{2} - 4350967625025 a + 9104523652009\) , \( 4936248025201452696 a^{2} + 7494205331413066679 a - 15681838058361251233\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-2865874952308a^{2}-4350967625025a+9104523652009\right){x}+4936248025201452696a^{2}+7494205331413066679a-15681838058361251233$ |
| 64.4-e4 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.987188848$ |
$6.937613183$ |
2.296370864 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 0\) , \( -182016 a^{2} - 276338 a + 578244\) , \( -79665661 a^{2} - 120948303 a + 253087768\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-182016a^{2}-276338a+578244\right){x}-79665661a^{2}-120948303a+253087768$ |
| 64.4-j2 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$7.266988548$ |
0.536824692 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} - 4\) , \( -78972 a^{2} - 119894 a + 250888\) , \( -22540110 a^{2} - 34220365 a + 71607092\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-78972a^{2}-119894a+250888\right){x}-22540110a^{2}-34220365a+71607092$ |
| 98.2-h4 |
98.2-h |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( - 2 \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.99138815$ |
2.068089108 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -1147925994504 a^{2} - 1742779751777 a + 3646816257396\) , \( 1251360661865905379 a^{2} + 1899814129232967219 a - 3975415163865073772\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-1147925994504a^{2}-1742779751777a+3646816257396\right){x}+1251360661865905379a^{2}+1899814129232967219a-3975415163865073772$ |
*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.
