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
39.1-a6
39.1-a
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( 3^{2} \cdot 13^{14} \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2Cs , 7B.6.3
$1$
\( 2^{2} \cdot 7 \)
$1$
$104.1126126$
0.953702256
\( -\frac{472782327302300801895731921547539}{35436387471293601} a^{4} + \frac{394975294976905362408499434574120}{11812129157097867} a^{3} + \frac{272811905305461777343354151432686}{11812129157097867} a^{2} - \frac{2778265732130705691487149505785760}{35436387471293601} a + \frac{933818725458499494056492136677657}{35436387471293601} \)
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2185 a^{4} - 6512 a^{3} - 2423 a^{2} + 15352 a - 7692\) , \( -148316 a^{4} + 370555 a^{3} + 276975 a^{2} - 864563 a + 250675\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(2185a^{4}-6512a^{3}-2423a^{2}+15352a-7692\right){x}-148316a^{4}+370555a^{3}+276975a^{2}-864563a+250675$
39.1-b6
39.1-b
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( 3^{2} \cdot 13^{14} \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2Cs , 7B.1.3
$2401$
\( 2^{2} \)
$1$
$0.477173882$
1.49927138
\( -\frac{472782327302300801895731921547539}{35436387471293601} a^{4} + \frac{394975294976905362408499434574120}{11812129157097867} a^{3} + \frac{272811905305461777343354151432686}{11812129157097867} a^{2} - \frac{2778265732130705691487149505785760}{35436387471293601} a + \frac{933818725458499494056492136677657}{35436387471293601} \)
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4889 a^{4} + 8124 a^{3} + 17837 a^{2} - 18525 a - 13048\) , \( -269334 a^{4} + 434813 a^{3} + 983058 a^{2} - 970083 a - 674066\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4889a^{4}+8124a^{3}+17837a^{2}-18525a-13048\right){x}-269334a^{4}+434813a^{3}+983058a^{2}-970083a-674066$
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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.