| 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 |
| 99.1-a1 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{24} \cdot 11^{2} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.403122864$ |
$1.883253066$ |
1.126738256 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -719488 a + 3374739\) , \( 240313509 a - 1127170198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-719488a+3374739\right){x}+240313509a-1127170198$ |
| 99.1-a2 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{12} \cdot 11^{4} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.701561432$ |
$7.533012266$ |
1.126738256 |
\( \frac{169112377}{88209} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 190652 a - 894196\) , \( 30744314 a - 144203543\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(190652a-894196\right){x}+30744314a-144203543$ |
| 99.1-a3 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{2} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.403122864$ |
$30.13204906$ |
1.126738256 |
\( \frac{30664297}{297} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -107901 a - 506100\) , \( 40976010 a + 192194523\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-107901a-506100\right){x}+40976010a+192194523$ |
| 99.1-a4 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.403122864$ |
$1.883253066$ |
1.126738256 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 2424632 a - 11372491\) , \( 4445368919 a - 20850628364\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2424632a-11372491\right){x}+4445368919a-20850628364$ |
| 99.1-b1 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{24} \cdot 11^{2} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.673520496$ |
$2.234063206$ |
4.452031855 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$ |
| 99.1-b2 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{12} \cdot 11^{4} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.336760248$ |
$8.936252827$ |
4.452031855 |
\( \frac{169112377}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$ |
| 99.1-b3 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{2} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.673520496$ |
$8.936252827$ |
4.452031855 |
\( \frac{30664297}{297} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$ |
| 99.1-b4 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(-a+5), (a+5), (7a-33)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.673520496$ |
$8.936252827$ |
4.452031855 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
*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.
