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
8.3-a1
8.3-a
$4$
$6$
3.3.316.1
$3$
$[3, 0]$
8.3
\( 2^{3} \)
\( - 2^{38} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$9$
\( 2 \)
$1$
$2.922549717$
0.739828198
\( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \)
\( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( -25 a^{2} + 70 a - 27\) , \( -153 a^{2} + 417 a - 163\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-25a^{2}+70a-27\right){x}-153a^{2}+417a-163$
32.5-b3
32.5-b
$4$
$6$
3.3.316.1
$3$
$[3, 0]$
32.5
\( 2^{5} \)
\( - 2^{38} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$28.54295458$
0.802833321
\( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \)
\( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( -27 a^{2} + 70 a - 18\) , \( 127 a^{2} - 348 a + 138\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-27a^{2}+70a-18\right){x}+127a^{2}-348a+138$
64.1-a2
64.1-a
$4$
$6$
3.3.316.1
$3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{50} \)
$3.17696$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$8.590621966$
1.449780725
\( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \)
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + 3\) , \( 0\) , \( -18 a^{2} + 42 a + 16\) , \( 44 a^{2} - 160 a + 76\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-18a^{2}+42a+16\right){x}+44a^{2}-160a+76$
128.7-a3
128.7-a
$4$
$6$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( - 2^{44} \)
$3.56602$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \cdot 5 \)
$0.054942025$
$13.32513593$
3.706596283
\( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 3\) , \( -873 a^{2} + 2452 a - 952\) , \( 30154 a^{2} - 84843 a + 33257\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(-873a^{2}+2452a-952\right){x}+30154a^{2}-84843a+33257$
128.7-f1
128.7-f
$4$
$6$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( - 2^{44} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \cdot 5 \)
$1$
$3.130107050$
2.641234178
\( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \)
\( \bigl[a^{2} - 3\) , \( -a\) , \( a^{2} + a - 2\) , \( -873 a^{2} + 2450 a - 955\) , \( -31027 a^{2} + 87293 a - 34213\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(-873a^{2}+2450a-955\right){x}-31027a^{2}+87293a-34213$
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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.