| 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 |
| 80.1-a1 |
80.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$10.34365470$ |
3.270950819 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-36{x}+140$ |
| 80.1-a2 |
80.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$10.34365470$ |
3.270950819 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+4{x}-4$ |
| 80.1-a3 |
80.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.68730941$ |
3.270950819 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 80.1-a4 |
80.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.68730941$ |
3.270950819 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 80.1-b1 |
80.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{8} \cdot 5^{8} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.933393502$ |
$8.151961419$ |
2.406173221 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}+6$ |
| 80.1-b2 |
80.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.866787005$ |
$32.60784567$ |
2.406173221 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-{x}$ |
| 80.1-b3 |
80.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.933393502$ |
$16.30392283$ |
2.406173221 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( -8\bigr] \) |
${y}^2={x}^{3}-8{x}-8$ |
| 80.1-b4 |
80.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.933393502$ |
$32.60784567$ |
2.406173221 |
\( \frac{132304644}{5} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -26\) , \( 40\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-26{x}+40$ |
| 80.1-c1 |
80.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.151961419$ |
1.288938274 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \) |
${y}^2={x}^{3}+13{x}+34$ |
| 80.1-c2 |
80.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.60784567$ |
1.288938274 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 80.1-c3 |
80.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.30392283$ |
1.288938274 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2={x}^{3}-2{x}-1$ |
| 80.1-c4 |
80.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.60784567$ |
1.288938274 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \) |
${y}^2={x}^{3}-107{x}+426$ |
| 80.1-d1 |
80.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.137812304$ |
$10.34365470$ |
1.352331812 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -7\) , \( 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-7{x}+9$ |
| 80.1-d2 |
80.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.413436914$ |
$10.34365470$ |
1.352331812 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+3{x}+1$ |
| 80.1-d3 |
80.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.206718457$ |
$20.68730941$ |
1.352331812 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-5{x}-5$ |
| 80.1-d4 |
80.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{20} \cdot 5^{6} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.068906152$ |
$20.68730941$ |
1.352331812 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 763\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-165{x}+763$ |
*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.
