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
5.1-a4
5.1-a
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
5.1
\( 5 \)
\( 5^{3} \)
$113.83972$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1[2]
$1$
\( 1 \)
$1$
$1682.101420$
1.50989
\( \frac{3288568389824}{25} a^{5} - \frac{1515811489972}{25} a^{4} - \frac{22321293042632}{25} a^{3} + \frac{3711500587103}{25} a^{2} + \frac{6892701907756}{5} a + \frac{7134572445643}{25} \)
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 42 a - 15\) , \( 5 a^{5} - 2 a^{4} - 34 a^{3} + 3 a^{2} + 53 a + 15\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( 12 a^{5} - 2 a^{4} - 86 a^{3} - 12 a^{2} + 146 a + 71\) , \( 80 a^{5} + 15 a^{4} - 507 a^{3} - 179 a^{2} + 627 a + 273\bigr] \)
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-42a-15\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-30a-12\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-34a^{3}+3a^{2}+53a+15\right){x}^{2}+\left(12a^{5}-2a^{4}-86a^{3}-12a^{2}+146a+71\right){x}+80a^{5}+15a^{4}-507a^{3}-179a^{2}+627a+273$
25.2-b4
25.2-b
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
25.2
\( 5^{2} \)
\( 5^{9} \)
$130.17912$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 5$
3B , 5B.1.1[2]
$1$
\( 2 \)
$1$
$25263.39045$
1.81415
\( \frac{3288568389824}{25} a^{5} - \frac{1515811489972}{25} a^{4} - \frac{22321293042632}{25} a^{3} + \frac{3711500587103}{25} a^{2} + \frac{6892701907756}{5} a + \frac{7134572445643}{25} \)
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( -6 a^{5} + 2 a^{4} + 41 a^{3} - a^{2} - 65 a - 21\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( -2 a^{5} - 3 a^{4} + 18 a^{3} + 16 a^{2} - 36 a - 16\) , \( -2 a^{5} - 2 a^{4} + 17 a^{3} + 16 a^{2} - 40 a - 20\bigr] \)
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-10\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+41a^{3}-a^{2}-65a-21\right){x}^{2}+\left(-2a^{5}-3a^{4}+18a^{3}+16a^{2}-36a-16\right){x}-2a^{5}-2a^{4}+17a^{3}+16a^{2}-40a-20$
405.2-m4
405.2-m
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
405.2
\( 3^{4} \cdot 5 \)
\( 3^{12} \cdot 5^{3} \)
$164.18529$
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 5$
3B.1.2 , 5B.4.1[2]
$9$
\( 1 \)
$1$
$101.9220910$
0.823385
\( \frac{3288568389824}{25} a^{5} - \frac{1515811489972}{25} a^{4} - \frac{22321293042632}{25} a^{3} + \frac{3711500587103}{25} a^{2} + \frac{6892701907756}{5} a + \frac{7134572445643}{25} \)
\( \bigl[a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 32 a - 10\) , \( -2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 22 a - 7\) , \( -4 a^{3} + 2 a^{2} + 15 a - 1\) , \( -68 a^{5} + 14 a^{4} + 473 a^{3} + 41 a^{2} - 758 a - 330\bigr] \)
${y}^2+\left(a^{5}-7a^{3}-a^{2}+11a+4\right){x}{y}+\left(-2a^{5}+a^{4}+14a^{3}-2a^{2}-22a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-32a-10\right){x}^{2}+\left(-4a^{3}+2a^{2}+15a-1\right){x}-68a^{5}+14a^{4}+473a^{3}+41a^{2}-758a-330$
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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.