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
64.4-a3
64.4-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.4
\( 2^{6} \)
\( 2^{8} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$14.31277055$
0.867839188
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 26\) , \( 33 a - 84\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-26\right){x}+33a-84$
64.4-b3
64.4-b
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.4
\( 2^{6} \)
\( 2^{8} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$28.03945840$
1.700141892
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 2\) , \( -3 a - 4\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-2\right){x}-3a-4$
128.6-a3
128.6-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.6
\( 2^{7} \)
\( 2^{14} \)
$1.23927$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$17.64735057$
2.140055600
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -49 a - 77\) , \( 220 a + 343\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-49a-77\right){x}+220a+343$
128.6-d3
128.6-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.6
\( 2^{7} \)
\( 2^{14} \)
$1.23927$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.163938021$
$34.57207326$
1.374613658
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( a - 8\) , \( -2 a + 4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-8\right){x}-2a+4$
512.1-e3
512.1-e
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{20} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$12.47856126$
1.513247827
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 71 a - 178\) , \( 444 a - 1136\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(71a-178\right){x}+444a-1136$
512.1-f3
512.1-f
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{20} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.471661635$
$24.44614744$
2.796510914
\( -\frac{159495}{4} a + 160181 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a - 10\) , \( 6 a + 16\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-10\right){x}+6a+16$
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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.