| 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 |
| 2116.5-a1 |
2116.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{20} \cdot 23^{2} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.327238898$ |
$2.403591625$ |
1.189149821 |
\( -\frac{116930169}{23552} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-10{x}-12$ |
| 2116.5-a2 |
2116.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{10} \cdot 23^{4} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.654477796$ |
$1.201795812$ |
1.189149821 |
\( \frac{545138290809}{16928} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-170{x}-812$ |
| 2116.5-b1 |
2116.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{10} \cdot 23^{4} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.530378571$ |
0.637595468 |
\( \frac{13554747117}{3114752} a - \frac{9754539647}{3114752} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 6 a - 1\) , \( 5 a + 13\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-1\right){x}+5a+13$ |
| 2116.5-b2 |
2116.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{5} \cdot 23^{8} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.265189285$ |
0.637595468 |
\( -\frac{1094442740089}{2368574224} a - \frac{738793867029}{2368574224} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -4 a - 21\) , \( 5 a + 61\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-21\right){x}+5a+61$ |
| 2116.5-b3 |
2116.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{30} \cdot 23^{4} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.843459523$ |
0.637595468 |
\( -\frac{94357520791587}{204128387072} a + \frac{479118885327985}{204128387072} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -54 a + 24\) , \( -104 a + 68\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-54a+24\right){x}-104a+68$ |
| 2116.5-b4 |
2116.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{15} \cdot 23^{8} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.421729761$ |
0.637595468 |
\( -\frac{785010145706635097}{606355001344} a + \frac{1046342212138057379}{606355001344} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -734 a + 264\) , \( -7320 a + 10084\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-734a+264\right){x}-7320a+10084$ |
| 2116.5-c1 |
2116.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{10} \cdot 23^{4} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.530378571$ |
0.637595468 |
\( -\frac{13554747117}{3114752} a + \frac{1900103735}{1557376} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -7 a + 5\) , \( -6 a + 18\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-7a+5\right){x}-6a+18$ |
| 2116.5-c2 |
2116.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{5} \cdot 23^{8} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.265189285$ |
0.637595468 |
\( \frac{1094442740089}{2368574224} a - \frac{916618303559}{1184287112} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 3 a - 25\) , \( -6 a + 66\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a-25\right){x}-6a+66$ |
| 2116.5-c3 |
2116.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{30} \cdot 23^{4} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.843459523$ |
0.637595468 |
\( \frac{94357520791587}{204128387072} a + \frac{192380682268199}{102064193536} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 53 a - 30\) , \( 103 a - 36\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(53a-30\right){x}+103a-36$ |
| 2116.5-c4 |
2116.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2116.5 |
\( 2^{2} \cdot 23^{2} \) |
\( 2^{15} \cdot 23^{8} \) |
$1.60349$ |
$(a), (-a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.421729761$ |
0.637595468 |
\( \frac{785010145706635097}{606355001344} a + \frac{130666033215711141}{303177500672} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 733 a - 470\) , \( 7319 a + 2764\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(733a-470\right){x}+7319a+2764$ |
*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.
