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 |
9075.5-a1 |
9075.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9075.5 |
\( 3 \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{5} \cdot 5^{6} \cdot 11^{9} \) |
$2.89265$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.078267626$ |
$0.538874465$ |
7.007737416 |
\( -\frac{2797353512}{151875} a - \frac{325474339}{50625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -182 a + 19\) , \( 1157 a - 1140\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-182a+19\right){x}+1157a-1140$ |
27225.8-c1 |
27225.8-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.8 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{11} \cdot 5^{6} \cdot 11^{3} \) |
$3.80695$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.031866042$ |
4.977909085 |
\( -\frac{2797353512}{151875} a - \frac{325474339}{50625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -48 a + 53\) , \( -37 a + 301\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-48a+53\right){x}-37a+301$ |
45375.6-a1 |
45375.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45375.6 |
\( 3 \cdot 5^{3} \cdot 11^{2} \) |
\( 3^{5} \cdot 5^{12} \cdot 11^{9} \) |
$4.32553$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.240991987$ |
1.162589090 |
\( -\frac{2797353512}{151875} a - \frac{325474339}{50625} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -117 a + 1588\) , \( -14372 a + 1486\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-117a+1588\right){x}-14372a+1486$ |
45375.7-f1 |
45375.7-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45375.7 |
\( 3 \cdot 5^{3} \cdot 11^{2} \) |
\( 3^{5} \cdot 5^{12} \cdot 11^{9} \) |
$4.32553$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.240991987$ |
1.453236362 |
\( -\frac{2797353512}{151875} a - \frac{325474339}{50625} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 298 a - 1610\) , \( -7156 a + 24381\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(298a-1610\right){x}-7156a+24381$ |
*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.