| 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 |
| 22275.1-a1 |
22275.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{8} \cdot 11^{3} \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.821696092$ |
0.495501387 |
\( \frac{53585}{121} a + \frac{497055}{121} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 29 a + 57\) , \( -66 a + 198\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a+57\right){x}-66a+198$ |
| 22275.1-a2 |
22275.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{4} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.465088277$ |
0.495501387 |
\( -\frac{32585}{11} a + \frac{82320}{11} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -6 a - 3\) , \( -9 a + 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-3\right){x}-9a+10$ |
| 22275.1-b1 |
22275.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{6} \cdot 5^{10} \cdot 11^{15} \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$6.185941732$ |
$0.098745448$ |
4.420158156 |
\( \frac{288322789502659}{133974300625} a - \frac{241975044280128}{133974300625} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2612 a - 4923\) , \( -96076 a + 130747\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2612a-4923\right){x}-96076a+130747$ |
| 22275.1-b2 |
22275.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{10} \cdot 5^{18} \cdot 11^{5} \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$18.55782519$ |
$0.032915149$ |
4.420158156 |
\( -\frac{4761132976229511855379}{324951171875} a + \frac{19904467562618343492243}{324951171875} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 205287 a - 422373\) , \( -69676884 a + 76785094\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(205287a-422373\right){x}-69676884a+76785094$ |
| 22275.1-c1 |
22275.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{6} \cdot 11 \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.592815284$ |
$1.590343894$ |
2.274071327 |
\( -\frac{6346}{11} a - \frac{36735}{11} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 10 a + 3\) , \( a - 67\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a+3\right){x}+a-67$ |
| 22275.1-d1 |
22275.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{3} \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$1.837368319$ |
3.323924355 |
\( \frac{53585}{121} a + \frac{497055}{121} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -10 a + 15\) , \( 4 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+15\right){x}+4a-30$ |
| 22275.1-d2 |
22275.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.1 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
$3.62067$ |
$(-a), (-a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$5.512104959$ |
3.323924355 |
\( -\frac{32585}{11} a + \frac{82320}{11} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 0\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+1$ |
*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.
