| 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-a3 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$3.960599634$ |
0.808454015 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 133 a - 326\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a+22\right){x}+133a-326$ |
| 10.2-b3 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 23\) , \( 2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(8a+23\right){x}+2a+7$ |
| 80.1-a3 |
80.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{21} \cdot 5^{9} \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$3.074662970$ |
1.255225901 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 34 a + 85\) , \( -17 a - 35\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(34a+85\right){x}-17a-35$ |
| 80.1-b3 |
80.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{21} \cdot 5^{9} \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.053388319$ |
$1.980299817$ |
1.553832031 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -36 a + 90\) , \( 1064 a - 2606\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-36a+90\right){x}+1064a-2606$ |
| 450.2-b3 |
450.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{9} \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.765090763$ |
$1.570369906$ |
1.962001293 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 25 a + 93\) , \( -50 a + 179\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a+93\right){x}-50a+179$ |
| 450.2-l3 |
450.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{9} \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.033939752$ |
3.798937226 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -568 a + 1387\) , \( 65545 a - 160555\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-568a+1387\right){x}+65545a-160555$ |
*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.
