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-b2
25.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( - 5^{12} \)
$1.07603$
$(-a-1), (-a+2)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$0.829376951$
$13.22753554$
1.358127807
\( \frac{22083041}{3125} a + \frac{239842001}{15625} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 7 a - 28\) , \( -69 a + 216\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(7a-28\right){x}-69a+216$
125.1-a2
125.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( - 5^{18} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$0.196588008$
$5.915533731$
2.591392545
\( \frac{22083041}{3125} a + \frac{239842001}{15625} \)
\( \bigl[a\) , \( a\) , \( a\) , \( -97 a - 217\) , \( 669 a + 1471\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-97a-217\right){x}+669a+1471$
125.2-b2
125.2-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( - 5^{18} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$5.915533731$
2.196974073
\( \frac{22083041}{3125} a + \frac{239842001}{15625} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -4 a - 37\) , \( -16 a + 152\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-37\right){x}-16a+152$
625.1-b2
625.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( - 5^{24} \)
$2.40607$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{4} \)
$1$
$2.645507109$
1.965033349
\( \frac{22083041}{3125} a + \frac{239842001}{15625} \)
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 194 a - 639\) , \( -8927 a + 28500\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(194a-639\right){x}-8927a+28500$
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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.