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
5491.1-a1
5491.1-a
$3$
$9$
\(\Q(\sqrt{-19}) \)
$2$
$[0, 1]$
5491.1
\( 17^{2} \cdot 19 \)
\( 17^{6} \cdot 19^{2} \)
$3.35296$
$(a+3), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cn , 3B
$1$
\( 2 \)
$8.069824998$
$0.226845754$
3.359757714
\( -\frac{50357871050752}{19} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -5385 a - 3079\) , \( -265648 a + 197882\bigr] \)
${y}^2+{y}={x}^3+a{x}^2+\left(-5385a-3079\right){x}-265648a+197882$
5491.1-a2
5491.1-a
$3$
$9$
\(\Q(\sqrt{-19}) \)
$2$
$[0, 1]$
5491.1
\( 17^{2} \cdot 19 \)
\( 17^{6} \cdot 19^{6} \)
$3.35296$
$(a+3), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cn , 3Cs
$1$
\( 2 \)
$2.689941666$
$0.680537264$
3.359757714
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -65 a - 39\) , \( -408 a + 377\bigr] \)
${y}^2+{y}={x}^3+a{x}^2+\left(-65a-39\right){x}-408a+377$
5491.1-a3
5491.1-a
$3$
$9$
\(\Q(\sqrt{-19}) \)
$2$
$[0, 1]$
5491.1
\( 17^{2} \cdot 19 \)
\( 17^{6} \cdot 19^{2} \)
$3.35296$
$(a+3), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cn , 3B
$1$
\( 2 \)
$0.896647222$
$2.041611794$
3.359757714
\( \frac{32768}{19} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 5 a + 1\) , \( 2 a - 8\bigr] \)
${y}^2+{y}={x}^3+a{x}^2+\left(5a+1\right){x}+2a-8$
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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.