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
22.1-b4
22.1-b
$4$
$6$
4.4.6809.1
$4$
$[4, 0]$
22.1
\( 2 \cdot 11 \)
\( - 2^{4} \cdot 11^{2} \)
$10.85133$
$(a+1), (a^3-5a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$772.3302456$
1.039965342
\( -\frac{2042536312629}{176} a^{3} + \frac{4227375539575}{176} a^{2} + \frac{365938930215}{44} a - \frac{89719838093}{16} \)
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a\) , \( -22 a^{3} - 45 a^{2} + 8 a + 16\) , \( -147 a^{3} - 331 a^{2} - 21 a + 71\bigr] \)
${y}^2+\left(a^{3}-5a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(-22a^{3}-45a^{2}+8a+16\right){x}-147a^{3}-331a^{2}-21a+71$
176.2-c1
176.2-c
$4$
$6$
4.4.6809.1
$4$
$[4, 0]$
176.2
\( 2^{4} \cdot 11 \)
\( - 2^{16} \cdot 11^{2} \)
$14.07244$
$(a+1), (a^3-5a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.395133653$
$115.7603833$
4.434577981
\( -\frac{2042536312629}{176} a^{3} + \frac{4227375539575}{176} a^{2} + \frac{365938930215}{44} a - \frac{89719838093}{16} \)
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{3} - 6 a\) , \( 0\) , \( -5 a^{3} - 13 a^{2} - 9 a\) , \( 19 a^{3} + 62 a^{2} + 53 a + 12\bigr] \)
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}={x}^{3}+\left(a^{3}-6a\right){x}^{2}+\left(-5a^{3}-13a^{2}-9a\right){x}+19a^{3}+62a^{2}+53a+12$
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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.