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-a3
39.1-a
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( - 3^{7} \cdot 13 \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.6.1
$1$
\( 1 \)
$1$
$2915.153153$
0.953702256
\( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \)
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 3\) , \( 4 a^{4} - 3 a^{3} - 15 a^{2} + 1\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+5a+3\right){x}+4a^{4}-3a^{3}-15a^{2}+1$
39.1-b3
39.1-b
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( - 3^{7} \cdot 13 \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.1.1
$1$
\( 7 \)
$1$
$8019.861435$
1.49927138
\( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \)
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4 a^{4} + 9 a^{3} + 12 a^{2} - 20 a - 3\) , \( 2 a^{4} - 9 a^{2} + 10\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4a^{4}+9a^{3}+12a^{2}-20a-3\right){x}+2a^{4}-9a^{2}+10$
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Pari/GP
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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.