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
8.1-a6
8.1-a
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{6} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$291.8773919$
0.684141088
\( \frac{113}{4} a^{2} - \frac{1939}{2} a + \frac{7773}{2} \)
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 587 a^{2} - 310 a - 2494\) , \( 8248 a^{2} - 4366 a - 35048\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(587a^{2}-310a-2494\right){x}+8248a^{2}-4366a-35048$
32.1-b8
32.1-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2 \)
$1$
$269.9496146$
1.898231533
\( \frac{113}{4} a^{2} - \frac{1939}{2} a + \frac{7773}{2} \)
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 170740 a^{2} - 90377 a - 725499\) , \( -39378439 a^{2} + 20843660 a + 167324520\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(170740a^{2}-90377a-725499\right){x}-39378439a^{2}+20843660a+167324520$
64.5-b6
64.5-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
64.5
\( 2^{6} \)
\( 2^{18} \)
$3.17696$
$(a), (-a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.134287355$
$129.5556641$
2.202066878
\( \frac{113}{4} a^{2} - \frac{1939}{2} a + \frac{7773}{2} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 5138 a^{2} - 2714 a - 21822\) , \( -210553 a^{2} + 111459 a + 894687\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(5138a^{2}-2714a-21822\right){x}-210553a^{2}+111459a+894687$
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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.