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
676.5-c1
676.5-c
$2$
$3$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{24} \cdot 13^{2} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \cdot 3^{2} \)
$0.016663791$
$11.19423574$
3.257439122
\( \frac{14967538313}{262144} a - \frac{38451438493}{262144} \)
\( \bigl[1\) , \( a\) , \( 0\) , \( 20 a - 52\) , \( -80 a + 208\bigr] \)
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(20a-52\right){x}-80a+208$
676.5-e1
676.5-e
$2$
$3$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{24} \cdot 13^{8} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$1$
$0.358962073$
1.044733091
\( \frac{14967538313}{262144} a - \frac{38451438493}{262144} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -2042 a - 3191\) , \( -161537 a - 252259\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2042a-3191\right){x}-161537a-252259$
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.