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
64.5-a4
64.5-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.5
\( 2^{6} \)
\( 2^{10} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$7.156385278$
0.867839188
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -171 a - 265\) , \( -1835 a - 2865\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-171a-265\right){x}-1835a-2865$
64.5-b4
64.5-b
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.5
\( 2^{6} \)
\( 2^{10} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$28.03945840$
1.700141892
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 15\) , \( -3 a + 11\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-15\right){x}-3a+11$
128.5-a4
128.5-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.5
\( 2^{7} \)
\( 2^{16} \)
$1.23927$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$4.411837643$
2.140055600
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 97 a - 256\) , \( 459 a - 1181\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(97a-256\right){x}+459a-1181$
128.5-d4
128.5-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.5
\( 2^{7} \)
\( 2^{16} \)
$1.23927$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.327876043$
$17.28603663$
1.374613658
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -33 a - 57\) , \( 141 a + 214\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-33a-57\right){x}+141a+214$
512.2-e4
512.2-e
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.2
\( 2^{9} \)
\( 2^{22} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.119640315$
1.513247827
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 768 a - 1968\) , \( 7764 a - 19888\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(768a-1968\right){x}+7764a-19888$
512.2-f4
512.2-f
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.2
\( 2^{9} \)
\( 2^{22} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.943323270$
$12.22307372$
2.796510914
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 55\) , \( 90 a + 54\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-55\right){x}+90a+54$
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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.