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-a2
16.4-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
16.4
\( 2^{4} \)
\( 2^{10} \)
$2.52156$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$116.1663040$
1.633716289
\( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \)
\( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 68 a^{2} - 44 a - 303\) , \( -73 a^{2} + 16 a + 269\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(68a^{2}-44a-303\right){x}-73a^{2}+16a+269$
32.5-a4
32.5-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
32.5
\( 2^{5} \)
\( 2^{10} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$135.2684195$
1.902360777
\( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \)
\( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 2\) , \( 68 a^{2} - 46 a - 306\) , \( 141 a^{2} - 62 a - 576\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(68a^{2}-46a-306\right){x}+141a^{2}-62a-576$
128.3-b2
128.3-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.3
\( 2^{7} \)
\( 2^{22} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$25.17046452$
1.415949254
\( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( 8 a^{2} + 14 a - 14\) , \( 8 a^{2} + 18 a - 10\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(8a^{2}+14a-14\right){x}+8a^{2}+18a-10$
128.7-b4
128.7-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{16} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$38.23073087$
1.075323318
\( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \)
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 217 a^{2} - 116 a - 921\) , \( -797 a^{2} + 421 a + 3386\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(217a^{2}-116a-921\right){x}-797a^{2}+421a+3386$
128.7-e2
128.7-e
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{16} \)
$3.56602$
$(a), (-a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.114549880$
$205.5104884$
1.986444107
\( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \)
\( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( 0\) , \( 215 a^{2} - 114 a - 914\) , \( 1013 a^{2} - 536 a - 4304\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(215a^{2}-114a-914\right){x}+1013a^{2}-536a-4304$
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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.