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
28.1-a1
28.1-a
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( - 2^{4} \cdot 7^{3} \)
$1.10695$
$(-a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$15.03985749$
1.396415711
\( -\frac{116300}{343} a + \frac{1485191}{1372} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}$
28.1-a2
28.1-a
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{6} \)
$1.10695$
$(-a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$15.03985749$
1.396415711
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8\) , \( -8 a + 6\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-8{x}-8a+6$
28.1-b1
28.1-b
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{12} \cdot 7^{4} \)
$1.10695$
$(-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \cdot 3 \)
$0.059060672$
$5.519552377$
1.452828972
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 3 a + 5\) , \( 22 a + 47\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+5\right){x}+22a+47$
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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.