| 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 |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
1.354107460 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
1.354107460 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
1.354107460 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
1.354107460 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.137812304$ |
$2.141031885$ |
1.679514028 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5\) , \( 25\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-5{x}+25$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.413436914$ |
$6.423095656$ |
1.679514028 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 5\) , \( -3\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+5{x}-3$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.826873828$ |
$6.423095656$ |
1.679514028 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \) |
${y}^2={x}^3+{x}^2-5{x}-5$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{6} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.275624609$ |
$2.141031885$ |
1.679514028 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 763\bigr] \) |
${y}^2={x}^3+{x}^2-165{x}+763$ |
*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.
