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
107.1-A1
107.1-A
$3$
$9$
3.1.23.1
$3$
$[1, 1]$
107.1
\( 107 \)
\( -107 \)
$0.93376$
$(5a^2-3a)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$72.11684248$
0.371293855
\( -\frac{36864}{107} a^{2} + \frac{102400}{107} a + \frac{61440}{107} \)
\( \bigl[0\) , \( a^{2} + a - 1\) , \( a^{2} + 1\) , \( a^{2} - a - 1\) , \( -a^{2}\bigr] \)
${y}^2+\left(a^{2}+1\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(a^{2}-a-1\right){x}-a^{2}$
107.1-A2
107.1-A
$3$
$9$
3.1.23.1
$3$
$[1, 1]$
107.1
\( 107 \)
\( - 107^{3} \)
$0.93376$
$(5a^2-3a)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$1$
$8.012982497$
0.371293855
\( -\frac{13431610740736}{1225043} a^{2} - \frac{34043228901376}{1225043} a - \frac{18044231077888}{1225043} \)
\( \bigl[0\) , \( a^{2} - a + 1\) , \( a^{2} + a\) , \( -30 a^{2} - 11 a + 11\) , \( -101 a^{2} + 29 a + 80\bigr] \)
${y}^2+\left(a^{2}+a\right){y}={x}^{3}+\left(a^{2}-a+1\right){x}^{2}+\left(-30a^{2}-11a+11\right){x}-101a^{2}+29a+80$
107.1-A3
107.1-A
$3$
$9$
3.1.23.1
$3$
$[1, 1]$
107.1
\( 107 \)
\( - 107^{9} \)
$0.93376$
$(5a^2-3a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$0.890331388$
0.371293855
\( -\frac{270815754742792058998784}{1838459212420154507} a^{2} + \frac{475186041093450994348032}{1838459212420154507} a - \frac{358714265350210784702464}{1838459212420154507} \)
\( \bigl[0\) , \( -a^{2} - a\) , \( 1\) , \( -59 a^{2} + 100 a - 71\) , \( -274 a^{2} + 484 a - 422\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a^{2}-a\right){x}^{2}+\left(-59a^{2}+100a-71\right){x}-274a^{2}+484a-422$
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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.