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
5.2-a1
5.2-a
$6$
$8$
3.3.940.1
$3$
$[3, 0]$
5.2
\( 5 \)
\( 5 \)
$3.58259$
$(-a^2+a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$20.50717563$
0.668870318
\( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \)
\( \bigl[a^{2} - a - 5\) , \( -a - 1\) , \( 1\) , \( 106 a^{2} - 63 a - 702\) , \( 1165 a^{2} - 702 a - 7734\bigr] \)
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a^{2}-63a-702\right){x}+1165a^{2}-702a-7734$
25.3-a6
25.3-a
$6$
$8$
3.3.940.1
$3$
$[3, 0]$
25.3
\( 5^{2} \)
\( 5^{7} \)
$4.68482$
$(-a^2+a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$0.731111200$
$9.171087748$
2.624349095
\( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \)
\( \bigl[1\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( -66 a^{2} + 151 a + 111\) , \( -562 a^{2} + 1296 a + 952\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-66a^{2}+151a+111\right){x}-562a^{2}+1296a+952$
80.10-c2
80.10-c
$6$
$8$
3.3.940.1
$3$
$[3, 0]$
80.10
\( 2^{4} \cdot 5 \)
\( 2^{12} \cdot 5 \)
$5.68701$
$(-a-2), (-a^2+a+5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.404497365$
$196.6656829$
1.945994544
\( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \)
\( \bigl[a^{2} - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 4\) , \( -898 a^{2} + 2066 a + 1544\) , \( 29347 a^{2} - 67286 a - 51176\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-898a^{2}+2066a+1544\right){x}+29347a^{2}-67286a-51176$
80.4-a1
80.4-a
$6$
$8$
3.3.940.1
$3$
$[3, 0]$
80.4
\( 2^{4} \cdot 5 \)
\( 2^{12} \cdot 5 \)
$5.68701$
$(a+1), (-a^2+a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$83.62073811$
2.727407748
\( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 208 a^{2} - 106 a - 1434\) , \( -3145 a^{2} + 1964 a + 20675\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(208a^{2}-106a-1434\right){x}-3145a^{2}+1964a+20675$
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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.