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
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$12.00303$
$(-a^2-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$343.2704704$
1.910717986
\( -\frac{526503}{25} a^{3} + \frac{958419}{25} a^{2} + \frac{2894547}{25} a - \frac{3922624}{25} \)
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 3 a^{3} - a^{2} - 14 a + 2\bigr] \)
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{3}+a^{2}-5a-4\right){x}+3a^{3}-a^{2}-14a+2$
25.1-a2
25.1-a
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{10} \)
$12.00303$
$(-a^2-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$171.6352352$
1.910717986
\( \frac{2937183550104}{625} a^{3} - \frac{3444473642517}{625} a^{2} - \frac{14095287030396}{625} a + \frac{17120317880357}{625} \)
\( \bigl[a^{3} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a + 5\) , \( a^{3} - 4 a + 1\) , \( -55 a^{3} - 69 a^{2} + 139 a + 36\) , \( 79 a^{3} + 85 a^{2} - 201 a - 31\bigr] \)
${y}^2+\left(a^{3}-3a+2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+5\right){x}^{2}+\left(-55a^{3}-69a^{2}+139a+36\right){x}+79a^{3}+85a^{2}-201a-31$
25.1-b1
25.1-b
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$12.00303$
$(-a^2-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$192.3156744$
1.070470809
\( -\frac{526503}{25} a^{3} + \frac{958419}{25} a^{2} + \frac{2894547}{25} a - \frac{3922624}{25} \)
\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a + 1\) , \( a^{2} + a - 3\) , \( 28 a^{3} + 7 a^{2} - 132 a - 25\) , \( 82 a^{3} + 20 a^{2} - 387 a - 72\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(28a^{3}+7a^{2}-132a-25\right){x}+82a^{3}+20a^{2}-387a-72$
25.1-b2
25.1-b
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{10} \)
$12.00303$
$(-a^2-a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$96.15783723$
1.070470809
\( \frac{2937183550104}{625} a^{3} - \frac{3444473642517}{625} a^{2} - \frac{14095287030396}{625} a + \frac{17120317880357}{625} \)
\( \bigl[a^{3} - 4 a + 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -42 a^{3} - 52 a^{2} + 99 a + 20\) , \( 228 a^{3} + 254 a^{2} - 600 a - 115\bigr] \)
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-42a^{3}-52a^{2}+99a+20\right){x}+228a^{3}+254a^{2}-600a-115$
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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.