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-a4
39.1-a
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( 3^{14} \cdot 13^{2} \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2Cs , 7B.6.1
$1$
\( 2^{2} \)
$1$
$728.7882883$
0.953702256
\( \frac{681363632760910}{808321761} a^{4} - \frac{50134304890058}{269440587} a^{3} - \frac{518208005828660}{269440587} a^{2} + \frac{361111060198751}{808321761} a + \frac{518784067066631}{808321761} \)
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -5 a^{4} - 2 a^{3} + 22 a^{2} + 2 a - 17\) , \( 10 a^{4} - 36 a^{3} - 41 a^{2} + 75 a + 25\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(-5a^{4}-2a^{3}+22a^{2}+2a-17\right){x}+10a^{4}-36a^{3}-41a^{2}+75a+25$
39.1-b4
39.1-b
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( 3^{14} \cdot 13^{2} \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z\oplus\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2Cs , 7B.1.1
$1$
\( 2^{2} \cdot 7 \)
$1$
$8019.861435$
1.49927138
\( \frac{681363632760910}{808321761} a^{4} - \frac{50134304890058}{269440587} a^{3} - \frac{518208005828660}{269440587} a^{2} + \frac{361111060198751}{808321761} a + \frac{518784067066631}{808321761} \)
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 8 a^{4} - 20 a^{3} - 18 a^{2} + 50 a - 15\) , \( -5 a^{4} + 14 a^{3} + 10 a^{2} - 35 a + 12\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(8a^{4}-20a^{3}-18a^{2}+50a-15\right){x}-5a^{4}+14a^{3}+10a^{2}-35a+12$
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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.