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-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
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 3 a + 5\) , \( 22 a + 47\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+5\right){x}+22a+47$
196.2-d1
196.2-d
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
196.2
\( 2^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 7^{10} \)
$1.80054$
$(-a), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \cdot 3 \)
$1$
$1.168485886$
2.603788581
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -3 a - 9\) , \( -651 a - 1429\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-9\right){x}-651a-1429$
700.4-i1
700.4-i
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.4
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{12} \cdot 5^{6} \cdot 7^{4} \)
$2.47521$
$(-a+2), (-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{3} \)
$0.508891561$
$2.468418864$
3.732201557
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 44 a - 143\) , \( 300 a - 958\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(44a-143\right){x}+300a-958$
700.6-h1
700.6-h
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.6
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{12} \cdot 5^{6} \cdot 7^{4} \)
$2.47521$
$(-a-1), (-a), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$1$
$2.468418864$
1.833495503
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \)
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( a - 12\) , \( 21 a - 16\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-12\right){x}+21a-16$
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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.