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
14.1-a1
14.1-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{5} \cdot 7 \)
$1.62148$
$(-3a-14), (-2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 5 \)
$0.248304172$
$11.35222992$
3.004857355
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a + 16\) , \( 2 a + 43\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+16\right){x}+2a+43$
14.1-b1
14.1-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{5} \cdot 7 \)
$1.62148$
$(-3a-14), (-2a+9)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$2.729835911$
$23.63686968$
1.528525378
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -640 a - 3000\) , \( 19709 a + 92440\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-640a-3000\right){x}+19709a+92440$
98.3-a1
98.3-a
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
98.3
\( 2 \cdot 7^{2} \)
\( 2^{5} \cdot 7^{7} \)
$2.63746$
$(-3a-14), (-2a+9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \cdot 5 \)
$1$
$2.783863877$
5.935217729
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -252 a + 1189\) , \( 27999 a - 131341\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-252a+1189\right){x}+27999a-131341$
98.3-b1
98.3-b
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
98.3
\( 2 \cdot 7^{2} \)
\( 2^{5} \cdot 7^{7} \)
$2.63746$
$(-3a-14), (-2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.861762187$
$13.76971982$
5.059774861
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -91 a - 429\) , \( 813 a + 3811\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-91a-429\right){x}+813a+3811$
112.2-c1
112.2-c
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
112.2
\( 2^{4} \cdot 7 \)
\( 2^{17} \cdot 7 \)
$2.72700$
$(-3a-14), (-2a+9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \)
$1$
$5.676114961$
2.420303551
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a + 17\) , \( -43 a + 206\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3a+17\right){x}-43a+206$
112.2-d1
112.2-d
$2$
$3$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
112.2
\( 2^{4} \cdot 7 \)
\( 2^{17} \cdot 7 \)
$2.72700$
$(-3a-14), (-2a+9)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.970087968$
$11.81843484$
4.888658928
\( -\frac{138599}{56} a - \frac{323739}{28} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2558 a - 11984\) , \( 152560 a + 715580\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-2558a-11984\right){x}+152560a+715580$
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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.