| 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 |
| 8379.1-a1 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{3} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.190951457$ |
$1.776165441$ |
2.349778965 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -17 a + 19\) , \( 11 a + 34\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17a+19\right){x}+11a+34$ |
| 8379.1-a2 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{6} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.095475728$ |
$0.888082720$ |
2.349778965 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 48 a + 9\) , \( -72 a + 239\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(48a+9\right){x}-72a+239$ |
| 8379.1-a3 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19 \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.572854372$ |
$1.776165441$ |
2.349778965 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -17 a + 4\) , \( 9 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-17a+4\right){x}+9a+1$ |
| 8379.1-a4 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{9} \cdot 7^{6} \cdot 19^{2} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$0.286427186$ |
$0.888082720$ |
2.349778965 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -212 a + 34\) , \( 1149 a - 785\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-212a+34\right){x}+1149a-785$ |
*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.
