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
16.1-a1
16.1-a
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
16.1
\( 2^{4} \)
\( 2^{9} \)
$2.52156$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$29.47640287$
1.658177211
\( \frac{63684217}{2} a^{2} - 89592107 a + 35115877 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{2} - 2\) , \( -3 a^{2} + 2 a + 9\) , \( -2 a^{2} + 3 a + 2\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-3a^{2}+2a+9\right){x}-2a^{2}+3a+2$
32.1-a1
32.1-a
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{9} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$72.47588334$
1.019271743
\( \frac{63684217}{2} a^{2} - 89592107 a + 35115877 \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( -602 a^{2} + 318 a + 2556\) , \( 12985 a^{2} - 6874 a - 55177\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-602a^{2}+318a+2556\right){x}+12985a^{2}-6874a-55177$
128.5-b6
128.5-b
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
128.5
\( 2^{7} \)
\( 2^{21} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1$
$85.44628392$
1.201682252
\( \frac{63684217}{2} a^{2} - 89592107 a + 35115877 \)
\( \bigl[0\) , \( a^{2} + a - 2\) , \( 0\) , \( -13733 a^{2} + 7272 a + 58358\) , \( 1468731 a^{2} - 777422 a - 6240841\bigr] \)
${y}^2={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-13733a^{2}+7272a+58358\right){x}+1468731a^{2}-777422a-6240841$
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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.