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
16.1-a3
16.1-a
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{16} \)
$0.81899$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 1 \)
$1$
$17.69503190$
0.965343132
\( 54000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 13\) , \( 11 a - 31\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-13\right){x}+11a-31$
16.1-a4
16.1-a
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{16} \)
$0.81899$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.2.1
$1$
\( 1 \)
$1$
$17.69503190$
0.965343132
\( 54000 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( -16 a - 28\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}-16a-28$
144.1-a3
144.1-a
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{6} \)
$1.41853$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
✓
$3, 7$
3B.1.2 , 7Ns.3.1
$1$
\( 2^{2} \cdot 3 \)
$0.263447686$
$5.898343969$
2.034539317
\( 54000 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -75 a - 135\) , \( -528 a - 946\bigr] \)
${y}^2={x}^{3}+\left(-75a-135\right){x}-528a-946$
144.1-a4
144.1-a
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{6} \)
$1.41853$
$(-a+2), (2)$
$1$
$\Z/6\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
✓
$3, 7$
3B.1.1 , 7Ns.3.1
$1$
\( 2^{2} \cdot 3 \)
$0.790343058$
$17.69503190$
2.034539317
\( 54000 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \)
${y}^2={x}^{3}-15{x}+22$
256.1-d3
256.1-d
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.63798$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.3.1
$1$
\( 1 \)
$1$
$17.69503190$
0.965343132
\( 54000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( 16 a + 28\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}+16a+28$
256.1-d4
256.1-d
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.63798$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Ns.3.1
$1$
\( 1 \)
$1$
$17.69503190$
0.965343132
\( 54000 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 13\) , \( -11 a + 31\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-13\right){x}-11a+31$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.