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
22.2-b3
22.2-b
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
22.2
\( 2 \cdot 11 \)
\( 2^{2} \cdot 11^{2} \)
$2.65901$
$(a), (a^2-a-1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$302.0639808$
1.062026656
\( -\frac{319453400201}{121} a^{2} + \frac{338230424177}{242} a + \frac{2714892100553}{242} \)
\( \bigl[1\) , \( a^{2} - a - 2\) , \( 0\) , \( 1111193215 a^{2} - 588174489 a - 4721618846\) , \( -29484933946309 a^{2} + 15606864446438 a + 125285628176318\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(1111193215a^{2}-588174489a-4721618846\right){x}-29484933946309a^{2}+15606864446438a+125285628176318$
176.2-a2
176.2-a
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
176.2
\( 2^{4} \cdot 11 \)
\( 2^{14} \cdot 11^{2} \)
$3.76040$
$(a), (a^2-a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1.465486159$
$27.46124150$
3.395858662
\( -\frac{319453400201}{121} a^{2} + \frac{338230424177}{242} a + \frac{2714892100553}{242} \)
\( \bigl[a\) , \( a^{2} - a - 2\) , \( a\) , \( 15864224246 a^{2} - 8397200243 a - 67409324365\) , \( 1590485002585538 a^{2} - 841870082167772 a - 6758194299506665\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(15864224246a^{2}-8397200243a-67409324365\right){x}+1590485002585538a^{2}-841870082167772a-6758194299506665$
242.4-d3
242.4-d
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
242.4
\( 2 \cdot 11^{2} \)
\( 2^{2} \cdot 11^{8} \)
$3.96538$
$(a), (a^2-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$42.06253278$
1.183101167
\( -\frac{319453400201}{121} a^{2} + \frac{338230424177}{242} a + \frac{2714892100553}{242} \)
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( 47773689714 a^{2} - 25287429738 a - 202997164562\) , \( -8311617833682939 a^{2} + 4399477124206896 a + 35317232269362968\bigr] \)
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(47773689714a^{2}-25287429738a-202997164562\right){x}-8311617833682939a^{2}+4399477124206896a+35317232269362968$
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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.