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-a1
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$3$
3Cs
$1$
\( 1 \)
$1$
$25.37997386$
1.295166367
\( 8000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 6 a - 16\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-6\right){x}+6a-16$
16.1-a2
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$3$
3Cs
$1$
\( 1 \)
$1$
$25.37997386$
1.295166367
\( 8000 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -6 a - 16\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-6\right){x}-6a-16$
16.1-a3
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$9$
\( 1 \)
$1$
$2.819997096$
1.295166367
\( -77092288000 a + 188837384000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 264 a - 646\) , \( 3782 a - 9264\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(264a-646\right){x}+3782a-9264$
16.1-a4
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$25.37997386$
1.295166367
\( -77092288000 a + 188837384000 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -64 a - 166\) , \( 418 a + 1056\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a-166\right){x}+418a+1056$
16.1-a5
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$25.37997386$
1.295166367
\( 77092288000 a + 188837384000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 64 a - 166\) , \( -418 a + 1056\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a-166\right){x}-418a+1056$
16.1-a6
16.1-a
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$0.87554$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$9$
\( 1 \)
$1$
$2.819997096$
1.295166367
\( 77092288000 a + 188837384000 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -264 a - 646\) , \( -3782 a - 9264\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-264a-646\right){x}-3782a-9264$
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*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.