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-a2
29.1-a
$2$
$7$
4.4.5125.1
$4$
$[4, 0]$
29.1
\( 29 \)
\( -29 \)
$9.74508$
$(a^3-4a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.6.1
$1$
\( 1 \)
$1$
$125.2260233$
1.749232970
\( \frac{1067314607}{29} a^{3} + \frac{130599537}{29} a^{2} - \frac{6126735575}{29} a - \frac{5531882051}{29} \)
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( 0\) , \( a^{3} - 4 a - 4\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{3} - 7 a - 7\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}+a^{3}-7a-7$
29.1-b2
29.1-b
$2$
$7$
4.4.5125.1
$4$
$[4, 0]$
29.1
\( 29 \)
\( -29 \)
$9.74508$
$(a^3-4a-4)$
$1$
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1.056492173$
$1661.600912$
2.001750670
\( \frac{1067314607}{29} a^{3} + \frac{130599537}{29} a^{2} - \frac{6126735575}{29} a - \frac{5531882051}{29} \)
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( -3 a^{3} + 7 a^{2} + 8 a - 18\) , \( 4 a^{3} - 14 a^{2} - 9 a + 43\bigr] \)
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-3a^{3}+7a^{2}+8a-18\right){x}+4a^{3}-14a^{2}-9a+43$
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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.