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-a4
25.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
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
\( \frac{9011529}{125} a + \frac{20092663}{125} \)
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -14 a - 30\) , \( 35 a + 76\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-14a-30\right){x}+35a+76$
125.1-b4
125.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( 5^{12} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$11.83106746$
2.196974073
\( \frac{9011529}{125} a + \frac{20092663}{125} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -8 a - 25\) , \( 17 a + 33\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-8a-25\right){x}+17a+33$
125.2-a4
125.2-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( 5^{12} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$0.393176016$
$11.83106746$
2.591392545
\( \frac{9011529}{125} a + \frac{20092663}{125} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 17 a - 40\) , \( 27 a - 73\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-40\right){x}+27a-73$
625.1-c4
625.1-c
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
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
\( \frac{9011529}{125} a + \frac{20092663}{125} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -315 a - 692\) , \( 4356 a + 9552\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-315a-692\right){x}+4356a+9552$
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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.