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-a3
64.5-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.5
\( 2^{6} \)
\( 2^{8} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$14.31277055$
0.867839188
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -11 a - 15\) , \( -33 a - 51\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-15\right){x}-33a-51$
64.5-b3
64.5-b
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
64.5
\( 2^{6} \)
\( 2^{8} \)
$1.04210$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$28.03945840$
1.700141892
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 5\) , \( 3 a - 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-5\right){x}+3a-7$
128.5-a3
128.5-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.5
\( 2^{7} \)
\( 2^{14} \)
$1.23927$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$17.64735057$
2.140055600
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 47 a - 126\) , \( -221 a + 563\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(47a-126\right){x}-221a+563$
128.5-d3
128.5-d
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
128.5
\( 2^{7} \)
\( 2^{14} \)
$1.23927$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.163938021$
$34.57207326$
1.374613658
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 7\) , \( a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-7\right){x}+a+2$
512.2-e3
512.2-e
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.2
\( 2^{9} \)
\( 2^{20} \)
$1.75259$
$(-a+2), (-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$12.47856126$
1.513247827
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a - 108\) , \( -374 a - 584\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a-108\right){x}-374a-584$
512.2-f3
512.2-f
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
512.2
\( 2^{9} \)
\( 2^{20} \)
$1.75259$
$(-a+2), (-a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.471661635$
$24.44614744$
2.796510914
\( \frac{159495}{4} a + \frac{481229}{4} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 15\) , \( -6 a + 22\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(5a-15\right){x}-6a+22$
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.