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-a4
25.1-a
$4$
$6$
6.6.1387029.1
$6$
$[6, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$137.61834$
$(a^3-a^2-3a)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$0.051491437$
$89837.74441$
2.61854
\( \frac{266828773549}{625} a^{4} - \frac{533657547098}{625} a^{3} - \frac{1120425675204}{625} a^{2} + \frac{1387254448753}{625} a + \frac{1343301833472}{625} \)
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} - 2\) , \( a^{3} - 3 a\) , \( -17 a^{5} + 50 a^{4} + 29 a^{3} - 131 a^{2} + 28 a + 2\) , \( 36 a^{5} - 117 a^{4} - 33 a^{3} + 298 a^{2} - 140 a + 17\bigr] \)
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}-2\right){x}^{2}+\left(-17a^{5}+50a^{4}+29a^{3}-131a^{2}+28a+2\right){x}+36a^{5}-117a^{4}-33a^{3}+298a^{2}-140a+17$
25.1-b4
25.1-b
$4$
$6$
6.6.1387029.1
$6$
$[6, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$137.61834$
$(a^3-a^2-3a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.065907809$
$13478.51203$
4.52572
\( \frac{266828773549}{625} a^{4} - \frac{533657547098}{625} a^{3} - \frac{1120425675204}{625} a^{2} + \frac{1387254448753}{625} a + \frac{1343301833472}{625} \)
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 6 a + 2\) , \( a\) , \( 3 a^{5} - 29 a^{4} + 3 a^{3} + 96 a^{2} - 5 a - 40\) , \( -73 a^{5} + 95 a^{4} + 223 a^{3} - 264 a^{2} - 102 a + 116\bigr] \)
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-6a+2\right){x}^{2}+\left(3a^{5}-29a^{4}+3a^{3}+96a^{2}-5a-40\right){x}-73a^{5}+95a^{4}+223a^{3}-264a^{2}-102a+116$
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Pari/GP
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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.