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
16.4-a1
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( - 2^{4} \)
$0.73687$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$9.235230655$
0.559968109
\( -7659605 a + 19620476 \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -a - 3\) , \( -6 a - 10\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-6a-10$
16.4-a2
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{11} \)
$0.73687$
$(-a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$18.47046131$
0.559968109
\( 343 a + 686 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
16.4-a3
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{10} \)
$0.73687$
$(-a+2)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$36.94092262$
0.559968109
\( -1995 a + 7016 \)
\( \bigl[a\) , \( a\) , \( a\) , \( -9 a - 15\) , \( -6 a - 10\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9a-15\right){x}-6a-10$
16.4-a4
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{8} \)
$0.73687$
$(-a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$18.47046131$
0.559968109
\( 24225 a + 44228 \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}$
16.4-a5
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{11} \)
$0.73687$
$(-a+2)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$36.94092262$
0.559968109
\( -21069823 a + 54821634 \)
\( \bigl[a\) , \( a\) , \( a\) , \( -124 a - 195\) , \( 916 a + 1430\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124a-195\right){x}+916a+1430$
16.4-a6
16.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( - 2^{10} \)
$0.73687$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$4.617615327$
0.559968109
\( 2701312025 a + 4218241728 \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( -5 a - 20\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4a{x}-5a-20$
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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.