| 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 |
| 873.1-a1 |
873.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{4} \cdot 97^{4} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.187029947$ |
2.894552196 |
\( \frac{94220968500736}{88529281} a - \frac{1199069572356032}{796763529} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 19 a + 8\) , \( 67 a + 141\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(19a+8\right){x}+67a+141$ |
| 873.1-a2 |
873.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{2} \cdot 97^{2} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.37405989$ |
2.894552196 |
\( -\frac{30155301398982144}{9409} a + \frac{127938108886869184}{28227} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -9 a - 91\) , \( 58 a + 303\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-9a-91\right){x}+58a+303$ |
| 873.1-b1 |
873.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{2} \cdot 97^{2} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.59242046$ |
3.109929952 |
\( -\frac{43179520}{28227} a + \frac{36659264}{9409} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 2 a - 4\) , \( 2 a - 3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(2a-4\right){x}+2a-3$ |
| 873.1-b2 |
873.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{4} \cdot 97 \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.59242046$ |
3.109929952 |
\( \frac{34164224}{291} a + \frac{154356800}{873} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 2 a - 5\) , \( -3 a + 3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(2a-5\right){x}-3a+3$ |
| 873.1-c1 |
873.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{8} \cdot 97^{2} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.072056099$ |
1.439689240 |
\( \frac{2135567104}{84681} a - \frac{27207662272}{762129} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 9\) , \( 12 a - 13\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-9\right){x}+12a-13$ |
| 873.1-c2 |
873.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{4} \cdot 97 \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.144112199$ |
1.439689240 |
\( -\frac{1604704631552}{873} a + \frac{252172311872}{97} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 18 a - 38\) , \( 67 a - 85\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(18a-38\right){x}+67a-85$ |
| 873.1-d1 |
873.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{2} \cdot 97^{2} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.213408683$ |
0.568055767 |
\( -\frac{36076356355072}{28227} a + \frac{17012659933248}{9409} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 66 a - 104\) , \( 371 a - 554\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(66a-104\right){x}+371a-554$ |
| 873.1-d2 |
873.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{4} \cdot 97 \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.213408683$ |
0.568055767 |
\( \frac{14393001790464}{97} a + \frac{183193058163776}{873} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 50\) , \( 13 a - 162\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-50\right){x}+13a-162$ |
| 873.1-e1 |
873.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{4} \cdot 97 \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.031394396$ |
1.066209969 |
\( -\frac{532136}{97} a - \frac{6416239}{873} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 1\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-1\right){x}-2$ |
| 873.1-e2 |
873.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
873.1 |
\( 3^{2} \cdot 97 \) |
\( 3^{2} \cdot 97^{2} \) |
$1.37384$ |
$(-7a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.031394396$ |
1.066209969 |
\( \frac{2503796216108}{28227} a + \frac{1180353969963}{9409} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 16\) , \( -6 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-16\right){x}-6a-20$ |
*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.
