| 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 |
| 99.3-a1 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{11} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -12 a - 90\) , \( 71 a + 302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-90\right){x}+71a+302$ |
| 99.3-a2 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{25} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( \frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a + 95\) , \( 251 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+95\right){x}+251a-30$ |
| 99.3-a3 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.394636825$ |
0.600092679 |
\( -\frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}+a+4$ |
| 99.3-a4 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.789273651$ |
0.600092679 |
\( \frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 99.3-a5 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{14} \cdot 11^{4} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8 a\) , \( 19 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+8a{x}+19a+22$ |
| 99.3-a6 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{7} \cdot 11^{8} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( -\frac{68547528581042953}{156267624249} a + \frac{367387425943146769}{156267624249} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 173 a - 15\) , \( 859 a + 1006\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(173a-15\right){x}+859a+1006$ |
*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.
