| 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 |
| 6498.1-a1 |
6498.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 19^{4} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.134767640$ |
$0.717655298$ |
1.934334224 |
\( -\frac{69173457625}{42633378} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -85\) , \( 473\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-85{x}+473$ |
| 6498.1-a2 |
6498.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 19^{2} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.269535280$ |
$1.435310597$ |
1.934334224 |
\( \frac{96386901625}{18468} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -95\) , \( -399\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-95{x}-399$ |
| 6498.1-b1 |
6498.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{12} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.404885376$ |
2.429312260 |
\( -\frac{8078253774625}{846825858} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \) |
${y}^2+{x}{y}={x}^{3}-418{x}-3610$ |
| 6498.1-b2 |
6498.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{4} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.214656130$ |
2.429312260 |
\( \frac{3616805375}{2105352} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+32{x}+8$ |
| 6498.1-b3 |
6498.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.429312260$ |
2.429312260 |
\( \frac{57066625}{32832} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-8{x}$ |
| 6498.1-b4 |
6498.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 19^{6} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.809770753$ |
2.429312260 |
\( \frac{8671983378625}{82308} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -428\) , \( 3444\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-428{x}+3444$ |
| 6498.1-c1 |
6498.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{10} \cdot 3^{24} \cdot 19^{8} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$1$ |
$0.110484662$ |
3.314539880 |
\( -\frac{16576888679672833}{2216253521952} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -5311\) , \( 167551\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-5311{x}+167551$ |
| 6498.1-c2 |
6498.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{40} \cdot 3^{6} \cdot 19^{2} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.441938650$ |
3.314539880 |
\( \frac{4824238966273}{537919488} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -351\) , \( 2431\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-351{x}+2431$ |
| 6498.1-c3 |
6498.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{20} \cdot 3^{12} \cdot 19^{4} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
$1$ |
$0.220969325$ |
3.314539880 |
\( \frac{18120364883707393}{269485056} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5472\) , \( -158079\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5472{x}-158079$ |
| 6498.1-c4 |
6498.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 19^{2} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$0.110484662$ |
3.314539880 |
\( \frac{74220219816682217473}{16416} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -87552\) , \( -10007679\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-87552{x}-10007679$ |
*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.
