| 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 |
| 800.1-a1 |
800.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{10} \) |
$3.00567$ |
$(2,a), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.808491475$ |
1.143790438 |
\( -320 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 30\) , \( 70 a\bigr] \) |
${y}^2={x}^3+a{x}^2+30{x}+70a$ |
| 800.1-b1 |
800.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.857218917$ |
$1.808491475$ |
3.921915202 |
\( -320 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5\) , \( 5 a\bigr] \) |
${y}^2={x}^3-a{x}^2+5{x}+5a$ |
| 800.1-c1 |
800.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{4} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns |
$1$ |
\( 2 \) |
$0.318472330$ |
$5.319699904$ |
2.142983515 |
\( -5000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -8\) , \( 8\bigr] \) |
${y}^2={x}^3+{x}^2-8{x}+8$ |
| 800.1-d1 |
800.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{4} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.218002349$ |
$5.319699904$ |
4.400778950 |
\( -5000 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 5\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+5{x}+5$ |
| 800.1-e1 |
800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.583123442$ |
$3.074676569$ |
6.157071676 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20\) , \( 0\bigr] \) |
${y}^2={x}^3+20{x}$ |
| 800.1-e2 |
800.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.583123442$ |
$3.074676569$ |
6.157071676 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( 0\bigr] \) |
${y}^2={x}^3-5{x}$ |
| 800.1-f1 |
800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.244048612$ |
$3.074676569$ |
4.363768417 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5\) , \( 0\bigr] \) |
${y}^2={x}^3+5{x}$ |
| 800.1-f2 |
800.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.122024306$ |
$3.074676569$ |
4.363768417 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^3-20{x}$ |
| 800.1-g1 |
800.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{4} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.160665614$ |
$5.319699904$ |
6.486662682 |
\( -5000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+7{x}+2$ |
| 800.1-h1 |
800.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{4} \) |
$3.00567$ |
$(2,a), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns |
$1$ |
\( 2 \) |
$1$ |
$5.319699904$ |
3.364473633 |
\( -5000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -8\bigr] \) |
${y}^2={x}^3-{x}^2-8{x}-8$ |
| 800.1-i1 |
800.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$3.00567$ |
$(2,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.857218917$ |
$1.808491475$ |
3.921915202 |
\( -320 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 5\) , \( -5 a\bigr] \) |
${y}^2={x}^3+a{x}^2+5{x}-5a$ |
| 800.1-j1 |
800.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
800.1 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{10} \) |
$3.00567$ |
$(2,a), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.808491475$ |
1.143790438 |
\( -320 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 30\) , \( -70 a\bigr] \) |
${y}^2={x}^3-a{x}^2+30{x}-70a$ |
*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.
