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
$2$
$3$
5.5.181057.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( - 5^{2} \)
$52.46144$
$(a^3-2a^2-3a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.014349913$
$21629.26971$
3.64714875
\( -\frac{48803087}{5} a^{4} + \frac{185083624}{5} a^{3} - 27082805 a^{2} - \frac{101317246}{5} a + \frac{82622024}{5} \)
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{2} - a - 1\) , \( -5 a^{4} + 3 a^{3} + 30 a^{2} - 7 a - 24\) , \( -a^{4} + a^{3} + 4 a^{2} - a + 7\bigr] \)
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-5a^{4}+3a^{3}+30a^{2}-7a-24\right){x}-a^{4}+a^{3}+4a^{2}-a+7$
25.1-a2
25.1-a
$2$
$3$
5.5.181057.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( - 5^{6} \)
$52.46144$
$(a^3-2a^2-3a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.043049739$
$7209.756571$
3.64714875
\( \frac{28069349767}{125} a^{4} - \frac{37403782797}{125} a^{3} - \frac{137248787392}{125} a^{2} + \frac{104873423319}{125} a + \frac{5046062774}{5} \)
\( \bigl[a^{3} - 3 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a\) , \( a^{4} - 5 a^{2} - 2 a + 4\) , \( -9 a^{4} - 3 a^{3} + 57 a^{2} + 32 a - 43\) , \( -50 a^{4} - 2 a^{3} + 282 a^{2} + 118 a - 194\bigr] \)
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{4}-5a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a\right){x}^{2}+\left(-9a^{4}-3a^{3}+57a^{2}+32a-43\right){x}-50a^{4}-2a^{3}+282a^{2}+118a-194$
25.1-b1
25.1-b
$1$
$1$
5.5.181057.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( - 5^{2} \)
$52.46144$
$(a^3-2a^2-3a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.010220239$
$14216.10920$
1.70727776
\( 7735 a^{4} - \frac{34594}{5} a^{3} - \frac{244456}{5} a^{2} + \frac{150814}{5} a + \frac{230852}{5} \)
\( \bigl[a^{3} - 4 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( 3 a^{4} - 4 a^{3} - 15 a^{2} + 11 a + 15\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){x}^{2}+\left(3a^{4}-4a^{3}-15a^{2}+11a+15\right){x}$
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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.