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
61.2-a1
61.2-a
$2$
$5$
5.5.24217.1
$5$
$[5, 0]$
61.2
\( 61 \)
\( 61 \)
$20.97644$
$(a^3+a^2-3a)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$5294.196281$
1.36081742
\( -\frac{115152428}{61} a^{4} - \frac{248328657}{61} a^{3} + \frac{38281223}{61} a^{2} + \frac{189872228}{61} a + \frac{54566560}{61} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 10 a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( 4 a^{4} - 2 a^{3} - 20 a^{2} + 6 a + 9\) , \( 2 a^{4} - 4 a^{3} - 7 a^{2} + 9 a + 4\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}-10a^{2}-a+4\right){x}^{2}+\left(4a^{4}-2a^{3}-20a^{2}+6a+9\right){x}+2a^{4}-4a^{3}-7a^{2}+9a+4$
61.2-a2
61.2-a
$2$
$5$
5.5.24217.1
$5$
$[5, 0]$
61.2
\( 61 \)
\( 61^{5} \)
$20.97644$
$(a^3+a^2-3a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$25$
\( 5 \)
$1$
$1.694142810$
1.36081742
\( \frac{947582806658950190622182}{226981} a^{4} - \frac{684924891007902588272712}{226981} a^{3} - \frac{4242841621501708043901758}{226981} a^{2} + \frac{2119197020585266574178655}{226981} a + \frac{1310965894310847398348250}{226981} \)
\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{4} - 5 a^{2} + 3\) , \( -33 a^{4} + 86 a^{3} + 225 a^{2} - 86 a - 137\) , \( -317 a^{4} + 1250 a^{3} + 1079 a^{2} - 939 a - 684\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(-33a^{4}+86a^{3}+225a^{2}-86a-137\right){x}-317a^{4}+1250a^{3}+1079a^{2}-939a-684$
61.2-b1
61.2-b
$1$
$1$
5.5.24217.1
$5$
$[5, 0]$
61.2
\( 61 \)
\( 61 \)
$20.97644$
$(a^3+a^2-3a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.004171145$
$13410.49608$
1.79725634
\( -\frac{23855802}{61} a^{4} + \frac{45097325}{61} a^{3} + \frac{29308428}{61} a^{2} - \frac{26625007}{61} a - \frac{11020762}{61} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( 3 a^{4} - 14 a^{2} - a + 3\) , \( a^{4} - 4 a^{2} + a\) , \( a^{4} - 4 a^{3} - 5 a^{2} + 14 a + 9\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(3a^{4}-14a^{2}-a+3\right){x}^{2}+\left(a^{4}-4a^{3}-5a^{2}+14a+9\right){x}+2a^{4}+a^{3}-10a^{2}-6a$
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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.