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
16.4-a1
16.4-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
16.4
\( 2^{4} \)
\( 2^{11} \)
$2.52156$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$14.52078800$
1.633716289
\( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \)
\( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 623 a^{2} - 449 a - 2863\) , \( 14329 a^{2} - 8700 a - 62909\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(623a^{2}-449a-2863\right){x}+14329a^{2}-8700a-62909$
32.5-a3
32.5-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
32.5
\( 2^{5} \)
\( 2^{11} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$135.2684195$
1.902360777
\( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \)
\( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 2\) , \( 623 a^{2} - 451 a - 2866\) , \( -13706 a^{2} + 8249 a + 60042\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(623a^{2}-451a-2866\right){x}-13706a^{2}+8249a+60042$
128.3-b1
128.3-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.3
\( 2^{7} \)
\( 2^{23} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$12.58523226$
1.415949254
\( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( 8 a^{2} - 6 a - 54\) , \( -128 a^{2} - 94 a + 246\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(8a^{2}-6a-54\right){x}-128a^{2}-94a+246$
128.7-b3
128.7-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{17} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$9.557682717$
1.075323318
\( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \)
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 2032 a^{2} - 1081 a - 8641\) , \( 71339 a^{2} - 37775 a - 303154\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2032a^{2}-1081a-8641\right){x}+71339a^{2}-37775a-303154$
128.7-e1
128.7-e
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{17} \)
$3.56602$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.229099761$
$102.7552442$
1.986444107
\( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \)
\( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( 0\) , \( 2030 a^{2} - 1079 a - 8634\) , \( -69308 a^{2} + 36695 a + 294516\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(2030a^{2}-1079a-8634\right){x}-69308a^{2}+36695a+294516$
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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.