| 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 |
| 85692.2-a1 |
85692.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{8} \cdot 3^{2} \cdot 37^{2} \cdot 193 \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.191104928$ |
$2.481484643$ |
4.380693155 |
\( \frac{24704904457}{12682416} a + \frac{311210239}{264217} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -10 a + 7\) , \( -3 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+7\right){x}-3a+9$ |
| 85692.2-a2 |
85692.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{4} \cdot 3 \cdot 37^{4} \cdot 193^{2} \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.191104928$ |
$1.240742321$ |
4.380693155 |
\( -\frac{759701280316513}{837727477068} a + \frac{1077380367825191}{837727477068} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 30 a - 13\) , \( -3 a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a-13\right){x}-3a+57$ |
| 85692.2-b1 |
85692.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{2} \cdot 3^{2} \cdot 37 \cdot 193^{6} \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.544212222$ |
2.513608583 |
\( -\frac{6291337183287813713}{11473524001933278} a + \frac{5028875320624316951}{3824508000644426} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -77 a + 161\) , \( -73 a + 563\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-77a+161\right){x}-73a+563$ |
| 85692.2-b2 |
85692.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{4} \cdot 3^{4} \cdot 37^{2} \cdot 193^{3} \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.088424444$ |
2.513608583 |
\( \frac{394554212929303}{354305485188} a + \frac{165293853132230}{88576371297} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 13 a - 49\) , \( -31 a + 95\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13a-49\right){x}-31a+95$ |
| 85692.2-c1 |
85692.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{8} \cdot 3^{2} \cdot 37^{4} \cdot 193^{3} \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.592052494$ |
2.734573338 |
\( \frac{4157757882043279}{646725612296496} a - \frac{4067523573515413}{215575204098832} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 34 a - 20\) , \( 642 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(34a-20\right){x}+642a+3$ |
| 85692.2-c2 |
85692.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
85692.2 |
\( 2^{2} \cdot 3 \cdot 37 \cdot 193 \) |
\( 2^{4} \cdot 3 \cdot 37^{2} \cdot 193^{6} \) |
$2.64810$ |
$(-2a+1), (-7a+4), (-16a+9), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.296026247$ |
2.734573338 |
\( -\frac{14523294806221066103663}{849040776143062572} a + \frac{60739205168374242673235}{424520388071531286} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1494 a - 960\) , \( 17906 a + 815\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1494a-960\right){x}+17906a+815$ |
*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.
