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
$2$
$2$
6.6.1081856.1
$6$
$[6, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$121.53973$
$(-a^5+5a^3+3a^2-4a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.172205993$
$5453.779711$
2.70883
\( -\frac{13234177536}{25} a^{5} + \frac{23027347904}{25} a^{4} + \frac{39338336256}{25} a^{3} - \frac{41983480576}{25} a^{2} - \frac{19581655424}{25} a + \frac{1520871744}{5} \)
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 5 a^{2} + 10 a - 2\) , \( -20 a^{5} + 25 a^{4} + 85 a^{3} - 65 a^{2} - 48 a + 15\) , \( -57 a^{5} + 79 a^{4} + 232 a^{3} - 211 a^{2} - 108 a + 40\bigr] \)
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+5a^{2}+10a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-20a^{5}+25a^{4}+85a^{3}-65a^{2}-48a+15\right){x}-57a^{5}+79a^{4}+232a^{3}-211a^{2}-108a+40$
25.1-a2
25.1-a
$2$
$2$
6.6.1081856.1
$6$
$[6, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$121.53973$
$(-a^5+5a^3+3a^2-4a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.086102996$
$5453.779711$
2.70883
\( \frac{209401250304}{625} a^{5} + \frac{57428760576}{625} a^{4} - \frac{1240676953472}{625} a^{3} - \frac{759032698048}{625} a^{2} + \frac{1257708985088}{625} a + \frac{763688663168}{625} \)
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -6 a^{5} + 8 a^{4} + 24 a^{3} - 18 a^{2} - 15 a + 4\) , \( -11 a^{5} + 15 a^{4} + 44 a^{3} - 37 a^{2} - 22 a + 6\bigr] \)
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}^{2}+\left(-6a^{5}+8a^{4}+24a^{3}-18a^{2}-15a+4\right){x}-11a^{5}+15a^{4}+44a^{3}-37a^{2}-22a+6$
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Pari/GP
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Magma
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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.