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-a1
25.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
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
\( -\frac{22083041}{3125} a + \frac{350257206}{15625} \)
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -9 a - 20\) , \( 68 a + 148\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-9a-20\right){x}+68a+148$
125.1-b1
125.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( - 5^{18} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$5.915533731$
2.196974073
\( -\frac{22083041}{3125} a + \frac{350257206}{15625} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 2 a - 40\) , \( 15 a + 136\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(2a-40\right){x}+15a+136$
125.2-a1
125.2-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( - 5^{18} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3 \)
$0.196588008$
$5.915533731$
2.591392545
\( -\frac{22083041}{3125} a + \frac{350257206}{15625} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 102 a - 310\) , \( -882 a + 2835\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(102a-310\right){x}-882a+2835$
625.1-c1
625.1-c
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
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
\( -\frac{22083041}{3125} a + \frac{350257206}{15625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -190 a - 442\) , \( 8481 a + 18677\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-190a-442\right){x}+8481a+18677$
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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.