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
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
29.1
\( 29 \)
\( - 29^{3} \)
$32.06409$
$(-2a^4+3a^3+8a^2-7a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.037391226$
$2117.436500$
1.54493280
\( \frac{3112416550238}{24389} a^{4} - \frac{4117133380738}{24389} a^{3} - \frac{14702539245891}{24389} a^{2} + \frac{10904653871054}{24389} a + \frac{14162641194095}{24389} \)
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( -6 a^{4} + 9 a^{3} + 25 a^{2} - 25 a - 16\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 11 a + 8\bigr] \)
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{4}+9a^{3}+25a^{2}-25a-16\right){x}+3a^{4}-5a^{3}-12a^{2}+11a+8$
261.1-a2
261.1-a
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
261.1
\( 3^{2} \cdot 29 \)
\( - 3^{6} \cdot 29^{3} \)
$39.94322$
$(-a^4+a^3+4a^2-2a-2), (-2a^4+3a^3+8a^2-7a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$9$
\( 1 \)
$1$
$79.88313084$
2.80580232
\( \frac{3112416550238}{24389} a^{4} - \frac{4117133380738}{24389} a^{3} - \frac{14702539245891}{24389} a^{2} + \frac{10904653871054}{24389} a + \frac{14162641194095}{24389} \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -a^{4} + 5 a^{2} - 2\) , \( 0\) , \( -7 a^{4} + 8 a^{3} + 34 a^{2} - 20 a - 27\) , \( -7 a^{4} + 5 a^{3} + 40 a^{2} - 11 a - 48\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-4\right){x}{y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(-7a^{4}+8a^{3}+34a^{2}-20a-27\right){x}-7a^{4}+5a^{3}+40a^{2}-11a-48$
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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.