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
28.2-a2
28.2-a
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
28.2
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{6} \)
$1.10695$
$(a-1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$15.03985749$
1.396415711
\( \frac{12890615364}{117649} a + \frac{9824768311}{33614} \)
\( \bigl[1\) , \( -a\) , \( 0\) , \( -8\) , \( 8 a - 2\bigr] \)
${y}^2+{x}{y}={x}^{3}-a{x}^{2}-8{x}+8a-2$
196.3-e2
196.3-e
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
196.3
\( 2^{2} \cdot 7^{2} \)
\( 2^{2} \cdot 7^{12} \)
$1.80054$
$(a-1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.382033532$
$9.812042810$
1.392168859
\( \frac{12890615364}{117649} a + \frac{9824768311}{33614} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 9 a - 84\) , \( -46 a + 246\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(9a-84\right){x}-46a+246$
700.3-g2
700.3-g
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.3
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{2} \cdot 5^{6} \cdot 7^{6} \)
$2.47521$
$(-a+2), (a-1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.826737063$
$6.726028744$
2.065176258
\( \frac{12890615364}{117649} a + \frac{9824768311}{33614} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -78 a - 170\) , \( 602 a + 1307\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-78a-170\right){x}+602a+1307$
700.5-g2
700.5-g
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.5
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{2} \cdot 5^{6} \cdot 7^{6} \)
$2.47521$
$(-a-1), (a-1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$6.726028744$
3.746976546
\( \frac{12890615364}{117649} a + \frac{9824768311}{33614} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 69 a - 229\) , \( 588 a - 1873\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(69a-229\right){x}+588a-1873$
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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.