| 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 |
| 10.2-a2 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -5 a + 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-3\right){x}-5a+12$ |
| 10.2-b2 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}-2a-4$ |
| 80.1-a2 |
80.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$3.074662970$ |
1.255225901 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6 a - 15\) , \( -9 a - 23\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-15\right){x}-9a-23$ |
| 80.1-b2 |
80.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{15} \cdot 5^{3} \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.017796106$ |
$17.82269835$ |
1.553832031 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4 a - 10\) , \( -40 a + 98\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(4a-10\right){x}-40a+98$ |
| 450.2-b2 |
450.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{9} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.255030254$ |
$4.711109719$ |
1.962001293 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -5 a - 12\) , \( 10 a + 14\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-12\right){x}+10a+14$ |
| 450.2-l2 |
450.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{9} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.101819256$ |
3.798937226 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 62 a - 158\) , \( -2465 a + 6035\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(62a-158\right){x}-2465a+6035$ |
*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.
