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
52.2-a2
52.2-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
52.2
\( 2^{2} \cdot 13 \)
\( 2^{5} \cdot 13^{2} \)
$0.98938$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$15.59610685$
1.260870508
\( -\frac{322217}{1352} a + \frac{424615}{676} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 3 a + 5\) , \( 50 a + 78\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a+5\right){x}+50a+78$
416.5-h2
416.5-h
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.5
\( 2^{5} \cdot 13 \)
\( 2^{17} \cdot 13^{2} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.207908848$
$9.444605334$
1.904988320
\( -\frac{322217}{1352} a + \frac{424615}{676} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -35 a + 92\) , \( -159 a + 408\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-35a+92\right){x}-159a+408$
416.7-b2
416.7-b
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
416.7
\( 2^{5} \cdot 13 \)
\( 2^{17} \cdot 13^{2} \)
$1.66393$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$4.897737670$
2.375751734
\( -\frac{322217}{1352} a + \frac{424615}{676} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 7 a + 11\) , \( -194 a - 303\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a+11\right){x}-194a-303$
676.5-a2
676.5-a
$4$
$6$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{5} \cdot 13^{8} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$1$
$3.290420844$
4.788265656
\( -\frac{322217}{1352} a + \frac{424615}{676} \)
\( \bigl[1\) , \( a\) , \( a\) , \( a + 7\) , \( -20 a - 31\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a+7\right){x}-20a-31$
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.