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
139.2-a1
139.2-a
$1$
$1$
4.4.725.1
$4$
$[4, 0]$
139.2
\( 139 \)
\( 139 \)
$4.45846$
$(a^3+a^2-2a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$26.07113072$
0.968257487
\( \frac{8850473917}{139} a^{3} - \frac{2509644061}{139} a^{2} - \frac{27960562523}{139} a - \frac{11810716302}{139} \)
\( \bigl[1\) , \( a^{3} - a^{2} - 2 a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( -4 a^{3} + 6 a^{2} + 9 a - 9\bigr] \)
${y}^2+{x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-4\right){x}-4a^{3}+6a^{2}+9a-9$
139.2-b1
139.2-b
$2$
$7$
4.4.725.1
$4$
$[4, 0]$
139.2
\( 139 \)
\( 139^{7} \)
$4.45846$
$(a^3+a^2-2a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 1 \)
$1$
$0.475474198$
0.865274752
\( \frac{28531033523895362170256351}{1002544368429379} a^{3} - \frac{7485122724910587730251117}{1002544368429379} a^{2} - \frac{91114676990285908071985197}{1002544368429379} a - \frac{38679901517361559411290561}{1002544368429379} \)
\( \bigl[a^{2} - 1\) , \( a^{2}\) , \( a^{3} - 3 a\) , \( 66 a^{3} - 29 a^{2} - 246 a - 130\) , \( 469 a^{3} - 262 a^{2} - 1781 a - 797\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+a^{2}{x}^{2}+\left(66a^{3}-29a^{2}-246a-130\right){x}+469a^{3}-262a^{2}-1781a-797$
139.2-b2
139.2-b
$2$
$7$
4.4.725.1
$4$
$[4, 0]$
139.2
\( 139 \)
\( 139 \)
$4.45846$
$(a^3+a^2-2a-4)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$1141.613550$
0.865274752
\( -\frac{54792}{139} a^{3} + \frac{8373}{139} a^{2} + \frac{166682}{139} a + \frac{74328}{139} \)
\( \bigl[a^{2} - 1\) , \( a^{2}\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - a\) , \( a^{3} + a^{2} - a - 1\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+a^{2}{x}^{2}+\left(a^{3}+a^{2}-a\right){x}+a^{3}+a^{2}-a-1$
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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.