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
36.2-a1
36.2-a
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
36.2
\( 2^{2} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$0.90248$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$7.698766537$
1.867225154
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 2 a + 3\) , \( 10 a + 15\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}+10a+15$
144.4-e1
144.4-e
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.4
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$1.27630$
$(-a+2), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.035029694$
$31.07619611$
1.056087100
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( 4 a - 8\) , \( -4 a + 8\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(4a-8\right){x}-4a+8$
324.2-b1
324.2-b
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
324.2
\( 2^{2} \cdot 3^{4} \)
\( 2^{8} \cdot 3^{14} \)
$1.56315$
$(-a+2), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \cdot 3 \)
$0.035019141$
$6.434945266$
1.311707883
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 9 a + 12\) , \( -236 a - 368\bigr] \)
${y}^2+a{y}={x}^{3}+\left(9a+12\right){x}-236a-368$
576.3-d1
576.3-d
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.3
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{2} \)
$1.80496$
$(-a+2), (-a-1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$1$
$2.391274390$
1.739907686
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 4\) , \( -35 a - 56\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(3a+4\right){x}-35a-56$
576.7-d1
576.7-d
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{2} \)
$1.80496$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$13.65058030$
3.310752026
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 46 a - 117\) , \( -208 a + 531\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-117\right){x}-208a+531$
576.7-o1
576.7-o
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{2} \)
$1.80496$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$3.381772674$
0.820200349
\( 77824 a - \frac{598016}{3} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( a - 1\) , \( -a - 5\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(a-1\right){x}-a-5$
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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.