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-a2
1.1-a
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
1.1
\( 1 \)
\( 1 \)
$58.90795$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 13$
3B , 13B.1.2
$28561$
\( 1 \)
$1$
$0.014802157$
0.641303
\( -299441694155033880148130654153024 a^{5} - 187917845986491657242090310571049 a^{4} + 704001225414123443403572247320027 a^{3} + 352597497846354900118604631201756 a^{2} - 271295440361411180696560081353475 a - 113961855027594415883614627224113 \)
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( 670 a^{5} - 2194 a^{4} + 16 a^{3} + 3065 a^{2} - 90 a - 1279\) , \( 20194 a^{5} - 68427 a^{4} + 14638 a^{3} + 73555 a^{2} - 10467 a - 21619\bigr] \)
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a-1\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-4a^{4}+11a^{2}-2a-3\right){x}^{2}+\left(670a^{5}-2194a^{4}+16a^{3}+3065a^{2}-90a-1279\right){x}+20194a^{5}-68427a^{4}+14638a^{3}+73555a^{2}-10467a-21619$
169.4-b2
169.4-b
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
169.4
\( 13^{2} \)
\( 13^{6} \)
$90.32982$
$(-a^2+a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 13$
3B , 13B.12.2
$169$
\( 1 \)
$1$
$6.191483410$
1.58725
\( -299441694155033880148130654153024 a^{5} - 187917845986491657242090310571049 a^{4} + 704001225414123443403572247320027 a^{3} + 352597497846354900118604631201756 a^{2} - 271295440361411180696560081353475 a - 113961855027594415883614627224113 \)
\( \bigl[2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 4 a\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 4 a^{2} - 4 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a + 1\) , \( 572 a^{5} - 1847 a^{4} - 189 a^{3} + 2641 a^{2} + 235 a - 1453\) , \( 29062 a^{5} - 85428 a^{4} - 21658 a^{3} + 132077 a^{2} - 1842 a - 34732\bigr] \)
${y}^2+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+4a\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-4a^{2}-4a-1\right){x}^{2}+\left(572a^{5}-1847a^{4}-189a^{3}+2641a^{2}+235a-1453\right){x}+29062a^{5}-85428a^{4}-21658a^{3}+132077a^{2}-1842a-34732$
169.5-b2
169.5-b
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
169.5
\( 13^{2} \)
\( 13^{6} \)
$90.32982$
$(-2a^5+5a^4+5a^3-11a^2-2a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 13$
3B , 13B.12.2
$169$
\( 1 \)
$1$
$6.191483410$
1.58725
\( -299441694155033880148130654153024 a^{5} - 187917845986491657242090310571049 a^{4} + 704001225414123443403572247320027 a^{3} + 352597497846354900118604631201756 a^{2} - 271295440361411180696560081353475 a - 113961855027594415883614627224113 \)
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 2\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a - 1\) , \( -4615 a^{5} + 6477 a^{4} + 22822 a^{3} - 9642 a^{2} - 26598 a - 8423\) , \( -357233 a^{5} + 457061 a^{4} + 1749388 a^{3} - 528206 a^{2} - 1762650 a - 502392\bigr] \)
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a\right){x}^{2}+\left(-4615a^{5}+6477a^{4}+22822a^{3}-9642a^{2}-26598a-8423\right){x}-357233a^{5}+457061a^{4}+1749388a^{3}-528206a^{2}-1762650a-502392$
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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.