| 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 |
| 5776.2-a1 |
5776.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$0.147598025$ |
$4.830783773$ |
1.008354273 |
\( -\frac{4194304}{19} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -5\) , \( -6\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-5{x}-6$ |
| 5776.2-b1 |
5776.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{10} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.062267605$ |
$4.606662983$ |
3.245290616 |
\( -\frac{31250}{19} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-2{x}-2$ |
| 5776.2-c1 |
5776.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.278258698$ |
$1.705295099$ |
2.684251981 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -62\) , \( 178\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-62{x}+178$ |
| 5776.2-c2 |
5776.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{66} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.504328284$ |
$0.189477233$ |
2.684251981 |
\( -\frac{69173457625}{2550136832} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -342\) , \( -19646\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-342{x}-19646$ |
| 5776.2-c3 |
5776.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{30} \cdot 19^{6} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.834776094$ |
$0.568431699$ |
2.684251981 |
\( \frac{94196375}{3511808} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 38\) , \( 722\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+38{x}+722$ |
| 5776.2-d1 |
5776.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{14} \cdot 19^{10} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.065585187$ |
$0.482527981$ |
4.475517586 |
\( -\frac{37966934881}{4952198} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -279\) , \( -1950\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-279{x}-1950$ |
| 5776.2-d2 |
5776.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{22} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.327925939$ |
$2.412639906$ |
4.475517586 |
\( -\frac{1}{608} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 1\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}+10$ |
| 5776.2-e1 |
5776.2-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$9.167331319$ |
$0.467654504$ |
6.062936882 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3077\) , \( -64681\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3077{x}-64681$ |
| 5776.2-e2 |
5776.2-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{6} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$3.055777106$ |
$1.402963512$ |
6.062936882 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -37\) , \( -81\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-37{x}-81$ |
| 5776.2-e3 |
5776.2-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.018592368$ |
$4.208890537$ |
6.062936882 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+3{x}-1$ |
| 5776.2-f1 |
5776.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$6.794444758$ |
4.804397963 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 0\) , \( 1\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+1$ |
*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.
