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
8.4-a1
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( - 2^{4} \)
$0.61963$
$(-a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( -7659605 a + 19620476 \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3 a - 11\) , \( -3 a + 6\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-11\right){x}-3a+6$
8.4-a2
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( 2^{11} \)
$0.61963$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.69057434$
0.769479095
\( 343 a + 686 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a + 13\) , \( 33 a - 86\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-6a+13\right){x}+33a-86$
8.4-a3
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( 2^{10} \)
$0.61963$
$(-a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( -1995 a + 7016 \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a\) , \( a\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+2a{x}+a$
8.4-a4
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( 2^{8} \)
$0.61963$
$(-a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$25.38114868$
0.769479095
\( 24225 a + 44228 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -14 a - 23\) , \( -47 a - 74\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-14a-23\right){x}-47a-74$
8.4-a5
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( 2^{11} \)
$0.61963$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.69057434$
0.769479095
\( -21069823 a + 54821634 \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 20\) , \( 15 a - 40\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-20\right){x}+15a-40$
8.4-a6
8.4-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
8.4
\( 2^{3} \)
\( - 2^{10} \)
$0.61963$
$(-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.345287171$
0.769479095
\( 2701312025 a + 4218241728 \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -80 a + 205\) , \( -1186 a + 3038\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-80a+205\right){x}-1186a+3038$
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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.