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
1.1-a4
1.1-a
$4$
$4$
5.5.179024.1
$5$
$[5, 0]$
1.1
\( 1 \)
\( 1 \)
$37.80891$
$\textsf{none}$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$0.068291357$
$4289.802622$
0.865480808
\( 1414198780324 a^{4} + 3815036657888 a^{3} - 1021893446812 a^{2} - 2756727621312 a + 1048460789992 \)
\( \bigl[3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 16\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 16 a + 14\) , \( a^{4} + a^{3} - 8 a^{2} - 7 a + 5\) , \( 16 a^{4} + 16 a^{3} - 125 a^{2} - 117 a + 73\) , \( -497 a^{4} - 266 a^{3} + 3815 a^{2} + 2050 a - 1754\bigr] \)
${y}^2+\left(3a^{4}+2a^{3}-24a^{2}-15a+16\right){x}{y}+\left(a^{4}+a^{3}-8a^{2}-7a+5\right){y}={x}^{3}+\left(3a^{4}+2a^{3}-24a^{2}-16a+14\right){x}^{2}+\left(16a^{4}+16a^{3}-125a^{2}-117a+73\right){x}-497a^{4}-266a^{3}+3815a^{2}+2050a-1754$
9.1-f4
9.1-f
$4$
$4$
5.5.179024.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( 3^{6} \)
$47.09973$
$(2a^4+a^3-15a^2-7a+7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$623.7333836$
2.94831143
\( 1414198780324 a^{4} + 3815036657888 a^{3} - 1021893446812 a^{2} - 2756727621312 a + 1048460789992 \)
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( 6 a^{4} + 3 a^{3} - 46 a^{2} - 23 a + 23\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( -239 a^{4} - 109 a^{3} + 1860 a^{2} + 854 a - 1040\) , \( 826 a^{4} + 381 a^{3} - 6440 a^{2} - 2952 a + 3605\bigr] \)
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}{y}+\left(-a^{4}+7a^{2}+a-1\right){y}={x}^{3}+\left(6a^{4}+3a^{3}-46a^{2}-23a+23\right){x}^{2}+\left(-239a^{4}-109a^{3}+1860a^{2}+854a-1040\right){x}+826a^{4}+381a^{3}-6440a^{2}-2952a+3605$
16.1-a4
16.1-a
$4$
$4$
5.5.179024.1
$5$
$[5, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$49.88916$
$(a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.204721517$
$6206.778241$
3.75391215
\( 1414198780324 a^{4} + 3815036657888 a^{3} - 1021893446812 a^{2} - 2756727621312 a + 1048460789992 \)
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -6 a^{4} - 3 a^{3} + 46 a^{2} + 23 a - 22\) , \( 0\) , \( -44 a^{4} + 38 a^{3} + 306 a^{2} - 258 a + 52\) , \( -109 a^{4} + 63 a^{3} + 774 a^{2} - 416 a + 27\bigr] \)
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}={x}^{3}+\left(-6a^{4}-3a^{3}+46a^{2}+23a-22\right){x}^{2}+\left(-44a^{4}+38a^{3}+306a^{2}-258a+52\right){x}-109a^{4}+63a^{3}+774a^{2}-416a+27$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.