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-a5
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
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.6.1
$4$
\( 1 \)
$1$
$182.1970720$
0.953702256
\( \frac{250577525153856331}{28431} a^{4} + \frac{23688817181716957}{9477} a^{3} - \frac{188375931275690315}{9477} a^{2} - \frac{51297605922912091}{28431} a + \frac{111644917373722610}{28431} \)
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 21 a^{4} + 48 a^{3} - 214 a^{2} - 40 a + 28\) , \( -319 a^{4} + 696 a^{3} + 155 a^{2} - 141 a + 20\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a\right){x}^{2}+\left(21a^{4}+48a^{3}-214a^{2}-40a+28\right){x}-319a^{4}+696a^{3}+155a^{2}-141a+20$
39.1-b5
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
$4$
\( 7 \)
$1$
$2004.965358$
1.49927138
\( \frac{250577525153856331}{28431} a^{4} + \frac{23688817181716957}{9477} a^{3} - \frac{188375931275690315}{9477} a^{2} - \frac{51297605922912091}{28431} a + \frac{111644917373722610}{28431} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( 120 a^{4} - 100 a^{3} - 445 a^{2} + 30 a + 42\) , \( 665 a^{4} - 538 a^{3} - 2479 a^{2} + 223 a + 422\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(120a^{4}-100a^{3}-445a^{2}+30a+42\right){x}+665a^{4}-538a^{3}-2479a^{2}+223a+422$
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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.