| 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 |
| 490.1-a1 |
490.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{2} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.572473402$ |
1.762170815 |
\( \frac{1367631}{2800} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 5\) , \( -15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+5{x}-15$ |
| 490.1-a2 |
490.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{8} \cdot 7^{4} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.572473402$ |
1.762170815 |
\( \frac{611960049}{122500} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -75\) , \( -223\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-75{x}-223$ |
| 490.1-a3 |
490.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{16} \cdot 7^{2} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$5.572473402$ |
1.762170815 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -355\) , \( 2185\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-355{x}+2185$ |
| 490.1-a4 |
490.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{4} \cdot 7^{8} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.393118350$ |
1.762170815 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1075\) , \( -14023\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-1075{x}-14023$ |
| 490.1-b1 |
490.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 7^{2} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.572473402$ |
0.881085407 |
\( \frac{1367631}{2800} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$ |
| 490.1-b2 |
490.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{4} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.572473402$ |
0.881085407 |
\( \frac{611960049}{122500} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-18{x}-19$ |
| 490.1-b3 |
490.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{16} \cdot 7^{2} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.572473402$ |
0.881085407 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-88{x}+317$ |
| 490.1-b4 |
490.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
490.1 |
\( 2 \cdot 5 \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{4} \cdot 7^{8} \) |
$2.65900$ |
$(2,a), (5,a), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.393118350$ |
0.881085407 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-268{x}-1619$ |
*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.
