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
14.2-a1
14.2-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{15} \cdot 7^{3} \)
$1.62148$
$(-3a-14), (2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \cdot 5 \)
$0.082768057$
$11.35222992$
3.004857355
\( -\frac{19062299657}{87808} a - \frac{44634002097}{43904} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -75 a - 348\) , \( 527 a + 2471\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-75a-348\right){x}+527a+2471$
14.2-a2
14.2-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{5} \cdot 7 \)
$1.62148$
$(-3a-14), (2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 5 \)
$0.248304172$
$11.35222992$
3.004857355
\( \frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a + 27\) , \( 14 a + 65\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+27\right){x}+14a+65$
14.2-b1
14.2-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{15} \cdot 7^{3} \)
$1.62148$
$(-3a-14), (2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$0.909945303$
$2.626318853$
1.528525378
\( -\frac{19062299657}{87808} a - \frac{44634002097}{43904} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -3221 a + 15105\) , \( -56343 a + 264264\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3221a+15105\right){x}-56343a+264264$
14.2-b2
14.2-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{5} \cdot 7 \)
$1.62148$
$(-3a-14), (2a+9)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$2.729835911$
$23.63686968$
1.528525378
\( \frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 639 a - 3000\) , \( -19710 a + 92440\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(639a-3000\right){x}-19710a+92440$
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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.