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-a2
25.1-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( - 5^{20} \)
$1.07603$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$2.488130854$
$1.469726171$
1.358127807
\( -\frac{55158051500782997}{3814697265625} a + \frac{176615422907709839}{3814697265625} \)
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 71 a + 145\) , \( -1764 a - 3893\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(71a+145\right){x}-1764a-3893$
125.1-b2
125.1-b
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.1
\( 5^{3} \)
\( - 5^{26} \)
$1.60903$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$9$
\( 2^{3} \)
$1$
$0.657281525$
2.196974073
\( -\frac{55158051500782997}{3814697265625} a + \frac{176615422907709839}{3814697265625} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 127 a - 165\) , \( -260 a - 4139\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(127a-165\right){x}-260a-4139$
125.2-a2
125.2-a
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
125.2
\( 5^{3} \)
\( - 5^{26} \)
$1.60903$
$(-a-1), (-a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \cdot 3^{2} \)
$0.589764025$
$0.657281525$
2.591392545
\( -\frac{55158051500782997}{3814697265625} a + \frac{176615422907709839}{3814697265625} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 1022 a - 3225\) , \( 28262 a - 90268\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1022a-3225\right){x}+28262a-90268$
625.1-c2
625.1-c
$4$
$6$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( - 5^{32} \)
$2.40607$
$(-a-1), (-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$9$
\( 2^{4} \)
$1$
$0.293945234$
1.965033349
\( -\frac{55158051500782997}{3814697265625} a + \frac{176615422907709839}{3814697265625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1810 a + 3683\) , \( -220394 a - 484823\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1810a+3683\right){x}-220394a-484823$
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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.