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-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
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8\) , \( -8 a + 6\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-8{x}-8a+6$
196.2-e2
196.2-e
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
196.2
\( 2^{2} \cdot 7^{2} \)
\( 2^{2} \cdot 7^{12} \)
$1.80054$
$(-a), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.382033532$
$9.812042810$
1.392168859
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -11 a - 75\) , \( 45 a + 200\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11a-75\right){x}+45a+200$
700.4-g2
700.4-g
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.4
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{2} \cdot 5^{6} \cdot 7^{6} \)
$2.47521$
$(-a+2), (-a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$6.726028744$
3.746976546
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \)
\( \bigl[a\) , \( 0\) , \( 1\) , \( -70 a - 159\) , \( -588 a - 1285\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-70a-159\right){x}-588a-1285$
700.6-g2
700.6-g
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
700.6
\( 2^{2} \cdot 5^{2} \cdot 7 \)
\( 2^{2} \cdot 5^{6} \cdot 7^{6} \)
$2.47521$
$(-a-1), (-a), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.826737063$
$6.726028744$
2.065176258
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 77 a - 248\) , \( -602 a + 1909\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(77a-248\right){x}-602a+1909$
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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.