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-a1
22.1-a
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
22.1
\( 2 \cdot 11 \)
\( 2^{4} \cdot 11^{2} \)
$1.44823$
$(-a+4), (a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.350694013$
$18.00713737$
1.687753482
\( \frac{69372345}{242} a - \frac{519137881}{484} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -28 a - 98\) , \( -2405 a - 8994\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-28a-98\right){x}-2405a-8994$
22.1-b1
22.1-b
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
22.1
\( 2 \cdot 11 \)
\( 2^{4} \cdot 11^{2} \)
$1.44823$
$(-a+4), (a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.845214156$
$7.121209110$
1.608631184
\( \frac{69372345}{242} a - \frac{519137881}{484} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3 a + 3\) , \( 3 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+3\right){x}+3a+7$
176.2-a1
176.2-a
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
176.2
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$2.43563$
$(-a+4), (a-5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.560604555$
0.951611595
\( \frac{69372345}{242} a - \frac{519137881}{484} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( 3 a - 17\) , \( 9 a - 32\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(3a-17\right){x}+9a-32$
176.2-d1
176.2-d
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
176.2
\( 2^{4} \cdot 11 \)
\( 2^{16} \cdot 11^{2} \)
$2.43563$
$(-a+4), (a-5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$9.003568687$
2.406304949
\( \frac{69372345}{242} a - \frac{519137881}{484} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -106 a - 381\) , \( -19129 a - 71557\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-106a-381\right){x}-19129a-71557$
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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.