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
72.4-a1
72.4-a
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
72.4
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{6} \)
$1.07324$
$(-a+2), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \cdot 3 \)
$0.005968972$
$24.61968422$
0.855399155
\( -\frac{80896}{9} a - \frac{388096}{27} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -29 a - 45\) , \( 115 a + 179\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-29a-45\right){x}+115a+179$
144.4-b1
144.4-b
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.4
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{6} \)
$1.27630$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$11.39664962$
2.764093541
\( -\frac{80896}{9} a - \frac{388096}{27} \)
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1\) , \( 2 a - 5\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}+2a-5$
576.7-a1
576.7-a
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{6} \)
$1.80496$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$1$
$5.184517639$
3.772290678
\( -\frac{80896}{9} a - \frac{388096}{27} \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -8 a - 13\) , \( -12 a - 19\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-13\right){x}-12a-19$
576.7-r1
576.7-r
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{6} \)
$1.80496$
$(-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$2.399954869$
0.582074554
\( -\frac{80896}{9} a - \frac{388096}{27} \)
\( \bigl[0\) , \( a\) , \( a\) , \( 10 a - 24\) , \( 54 a - 140\bigr] \)
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(10a-24\right){x}+54a-140$
648.4-a1
648.4-a
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
648.4
\( 2^{3} \cdot 3^{4} \)
\( 2^{8} \cdot 3^{18} \)
$1.85890$
$(-a+2), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{3} \)
$1.208013344$
$1.131349575$
5.303518302
\( -\frac{80896}{9} a - \frac{388096}{27} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( -261 a - 408\) , \( -3373 a - 5268\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-261a-408\right){x}-3373a-5268$
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.