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-a3
1.1-a
$4$
$39$
6.6.434581.1
$6$
$[6, 0]$
1.1
\( 1 \)
\( 1 \)
$58.90795$
$\textsf{none}$
0
$\Z/13\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 13$
3B , 13B.1.1
$1$
\( 1 \)
$1$
$71447.18768$
0.641303
\( 7824861 a^{5} - 5363852 a^{4} - 38334375 a^{3} - 11300754 a^{2} + 16416844 a + 5946574 \)
\( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 2\) , \( -3 a^{4} + 4 a^{3} + 12 a^{2} - 3 a - 4\) , \( 10 a^{5} - 28 a^{4} - 19 a^{3} + 67 a^{2} - 8 a - 15\bigr] \)
${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+12a^{2}-3a-4\right){x}+10a^{5}-28a^{4}-19a^{3}+67a^{2}-8a-15$
169.4-b3
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.12.1
$1$
\( 1 \)
$1$
$1046.360696$
1.58725
\( 7824861 a^{5} - 5363852 a^{4} - 38334375 a^{3} - 11300754 a^{2} + 16416844 a + 5946574 \)
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 3\) , \( 5 a^{5} - 14 a^{4} - 7 a^{3} + 31 a^{2} - 6 a - 6\) , \( 10 a^{5} - 24 a^{4} - 29 a^{3} + 64 a^{2} + 9 a - 23\bigr] \)
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+2\right){x}^{2}+\left(5a^{5}-14a^{4}-7a^{3}+31a^{2}-6a-6\right){x}+10a^{5}-24a^{4}-29a^{3}+64a^{2}+9a-23$
169.5-b3
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.12.1
$1$
\( 1 \)
$1$
$1046.360696$
1.58725
\( 7824861 a^{5} - 5363852 a^{4} - 38334375 a^{3} - 11300754 a^{2} + 16416844 a + 5946574 \)
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 14 a^{2} + a + 5\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( 2 a^{5} + 3 a^{4} - 17 a^{3} - 17 a^{2} + 10 a + 7\) , \( 17 a^{5} - 11 a^{4} - 85 a^{3} - 26 a^{2} + 38 a + 14\bigr] \)
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-2\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-2\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+3a^{3}-14a^{2}+a+5\right){x}^{2}+\left(2a^{5}+3a^{4}-17a^{3}-17a^{2}+10a+7\right){x}+17a^{5}-11a^{4}-85a^{3}-26a^{2}+38a+14$
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Pari/GP
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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.