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
29.1-a1
29.1-a
$1$
$1$
5.5.24217.1
$5$
$[5, 0]$
29.1
\( 29 \)
\( -29 \)
$19.47325$
$(-2a^4+a^3+10a^2-2a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$205.4596656$
1.32028110
\( -\frac{3576764830}{29} a^{4} - \frac{6949922095}{29} a^{3} + 85021120 a^{2} + \frac{4914209131}{29} a + \frac{615642891}{29} \)
\( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( -2 a^{4} + 9 a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3\) , \( -6 a^{4} - 3 a^{3} + 23 a^{2} + 15 a + 1\) , \( -6 a^{4} - 7 a^{3} + 19 a^{2} + 20 a + 4\bigr] \)
${y}^2+\left(2a^{4}-9a^{2}+2\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(-2a^{4}+9a^{2}+a-1\right){x}^{2}+\left(-6a^{4}-3a^{3}+23a^{2}+15a+1\right){x}-6a^{4}-7a^{3}+19a^{2}+20a+4$
29.1-b1
29.1-b
$2$
$7$
5.5.24217.1
$5$
$[5, 0]$
29.1
\( 29 \)
\( - 29^{7} \)
$19.47325$
$(-2a^4+a^3+10a^2-2a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$49$
\( 7 \)
$1$
$0.436965764$
0.963122128
\( -\frac{1081740781776866294940863471759}{17249876309} a^{4} + \frac{2120240724895871393224432246770}{17249876309} a^{3} + \frac{43206056991447348862819034032}{594823321} a^{2} - \frac{1374124848200655188432751002870}{17249876309} a - \frac{551901067153896026723504870757}{17249876309} \)
\( \bigl[a^{4} - 4 a^{2}\) , \( -3 a^{4} + 14 a^{2} + a - 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 262 a^{4} - 221 a^{3} - 1174 a^{2} + 730 a + 366\) , \( 3311 a^{4} - 2134 a^{3} - 14758 a^{2} + 6316 a + 3956\bigr] \)
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(2a^{4}-9a^{2}+2\right){y}={x}^{3}+\left(-3a^{4}+14a^{2}+a-4\right){x}^{2}+\left(262a^{4}-221a^{3}-1174a^{2}+730a+366\right){x}+3311a^{4}-2134a^{3}-14758a^{2}+6316a+3956$
29.1-b2
29.1-b
$2$
$7$
5.5.24217.1
$5$
$[5, 0]$
29.1
\( 29 \)
\( -29 \)
$19.47325$
$(-2a^4+a^3+10a^2-2a-4)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$7344.083601$
0.963122128
\( \frac{8427382}{29} a^{4} + \frac{7718790}{29} a^{3} - 1223286 a^{2} - \frac{41118125}{29} a - \frac{10576765}{29} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 6\) , \( 2 a^{4} - 9 a^{2} + 3\) , \( -a^{4} + 4 a^{2} - 1\) , \( -a^{2} - a\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(2a^{4}-9a^{2}+3\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-6\right){x}^{2}+\left(-a^{4}+4a^{2}-1\right){x}-a^{2}-a$
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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.