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-b1
25.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( 5^{6} \)
$1.07603$
$(-a-1), (-a+2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1.658753902$
$26.45507109$
1.358127807
\( -\frac{9011529}{125} a + \frac{29104192}{125} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 43\) , \( -36 a + 111\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(12a-43\right){x}-36a+111$
125.1-a1
125.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( 5^{12} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$0.393176016$
$11.83106746$
2.591392545
\( -\frac{9011529}{125} a + \frac{29104192}{125} \)
\( \bigl[a\) , \( a\) , \( a\) , \( -12 a - 32\) , \( -55 a - 118\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-12a-32\right){x}-55a-118$
125.2-b1
125.2-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( 5^{12} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$11.83106746$
2.196974073
\( -\frac{9011529}{125} a + \frac{29104192}{125} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 6 a - 32\) , \( -18 a + 51\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-32\right){x}-18a+51$
625.1-b1
625.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( 5^{18} \)
$2.40607$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$5.291014218$
1.965033349
\( -\frac{9011529}{125} a + \frac{29104192}{125} \)
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 319 a - 1014\) , \( -5052 a + 16125\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(319a-1014\right){x}-5052a+16125$
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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.