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-a1
64.4-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.4
\( 2^{6} \)
\( 2^{13} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$7.156385278$
0.867839188
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 0\) , \( -2 a - 4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-2a-4$
64.4-b1
64.4-b
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.4
\( 2^{6} \)
\( 2^{13} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$14.01972920$
1.700141892
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( -3 a + 6\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}-3{x}-3a+6$
128.6-a1
128.6-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.6
\( 2^{7} \)
\( 2^{19} \)
$1.23927$
$(-a+2), (-a-1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1$
$8.823675287$
2.140055600
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[a\) , \( a\) , \( a\) , \( a\) , \( a\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+a{x}+a$
128.6-d1
128.6-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.6
\( 2^{7} \)
\( 2^{19} \)
$1.23927$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.081969010$
$17.28603663$
1.374613658
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -a\) , \( 197 a + 308\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}-a{x}+197a+308$
512.1-e1
512.1-e
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{25} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.239280630$
1.513247827
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 8 a + 12\bigr] \)
${y}^2={x}^{3}+{x}^{2}+8a+12$
512.1-f1
512.1-f
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.1
\( 2^{9} \)
\( 2^{25} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.235830817$
$12.22307372$
2.796510914
\( \frac{217}{16} a - \frac{139}{4} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 12\) , \( -50 a + 128\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-12\right){x}-50a+128$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.