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
25.1-b4
25.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( 5^{10} \)
$1.07603$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 1 \)
$4.976261708$
$2.939452343$
1.358127807
\( \frac{2164654005908433}{1953125} a + \frac{4746203093393263}{1953125} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 57 a - 198\) , \( 397 a - 1296\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(57a-198\right){x}+397a-1296$
125.1-a4
125.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( 5^{16} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3^{2} \)
$1.179528050$
$1.314563051$
2.591392545
\( \frac{2164654005908433}{1953125} a + \frac{4746203093393263}{1953125} \)
\( \bigl[a\) , \( a\) , \( a\) , \( -1007 a - 2227\) , \( -30671 a - 67269\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-1007a-2227\right){x}-30671a-67269$
125.2-b4
125.2-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( 5^{16} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$9$
\( 2^{2} \)
$1$
$1.314563051$
2.196974073
\( \frac{2164654005908433}{1953125} a + \frac{4746203093393263}{1953125} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -44 a - 307\) , \( -448 a - 2164\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-44a-307\right){x}-448a-2164$
625.1-b4
625.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( 5^{22} \)
$2.40607$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$9$
\( 2^{3} \)
$1$
$0.587890468$
1.965033349
\( \frac{2164654005908433}{1953125} a + \frac{4746203093393263}{1953125} \)
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 1444 a - 4889\) , \( 46823 a - 152000\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1444a-4889\right){x}+46823a-152000$
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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.