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
4.3-a2
4.3-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
4.3
\( 2^{2} \)
\( - 2^{8} \)
$2.00136$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$98.10329547$
1.379685384
\( 510768 a^{2} - 1452320 a + 597920 \)
\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( a + 1\) , \( 32 a^{2} - 8 a - 120\) , \( 138 a^{2} - 59 a - 561\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(32a^{2}-8a-120\right){x}+138a^{2}-59a-561$
16.5-a1
16.5-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
16.5
\( 2^{4} \)
\( - 2^{8} \)
$2.52156$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$152.8488957$
2.149605541
\( 510768 a^{2} - 1452320 a + 597920 \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 29 a^{2} - 12 a - 116\) , \( -136 a^{2} + 77 a + 587\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(29a^{2}-12a-116\right){x}-136a^{2}+77a+587$
64.1-c2
64.1-c
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.1
\( 2^{6} \)
\( - 2^{20} \)
$3.17696$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 3 \)
$1$
$32.45491701$
1.369298792
\( 510768 a^{2} - 1452320 a + 597920 \)
\( \bigl[0\) , \( -a^{2} - a + 2\) , \( 0\) , \( -10 a^{2} + 8 a - 1\) , \( -31 a^{2} + 19 a - 2\bigr] \)
${y}^2={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-10a^{2}+8a-1\right){x}-31a^{2}+19a-2$
64.7-c1
64.7-c
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.7
\( 2^{6} \)
\( - 2^{14} \)
$3.17696$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$28.28981181$
0.795713124
\( 510768 a^{2} - 1452320 a + 597920 \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{2} - 3\) , \( 3 a^{2} + a - 5\) , \( -2 a^{2} - 4 a\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(3a^{2}+a-5\right){x}-2a^{2}-4a$
64.7-e2
64.7-e
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.7
\( 2^{6} \)
\( - 2^{14} \)
$3.17696$
$(-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.025624968$
$265.0243926$
1.146111581
\( 510768 a^{2} - 1452320 a + 597920 \)
\( \bigl[a^{2} + a - 2\) , \( a\) , \( a^{2} - 3\) , \( 4 a^{2} + 3 a - 7\) , \( 4 a^{2} + 5 a - 4\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(4a^{2}+3a-7\right){x}+4a^{2}+5a-4$
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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.