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-b1
14.1-b
$6$
$18$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{48} \cdot 7^{2} \)
$2.24040$
$(2,a), (a+7)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3^{2} \)
$1$
$7.027708105$
1.084398903
\( -\frac{548347731625}{1835008} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -35476 a - 229804\) , \( 9223680 a + 59776488\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35476a-229804\right){x}+9223680a+59776488$
14.1-c1
14.1-c
$6$
$18$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{36} \cdot 7^{2} \)
$2.24040$
$(2,a), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$3.484059793$
$7.027708105$
3.778110619
\( -\frac{548347731625}{1835008} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8871 a - 57416\) , \( 1135220 a + 7357190\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8871a-57416\right){x}+1135220a+7357190$
14.1-j1
14.1-j
$6$
$18$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{36} \cdot 7^{2} \)
$2.24040$
$(2,a), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$26.30318993$
$0.436190660$
1.770354089
\( -\frac{548347731625}{1835008} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
14.1-k1
14.1-k
$6$
$18$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{48} \cdot 7^{2} \)
$2.24040$
$(2,a), (a+7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$9$
\( 2^{3} \cdot 3^{2} \)
$1$
$0.436190660$
5.451760094
\( -\frac{548347731625}{1835008} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -23905663 a - 154926339\) , \( -162458649312 a - 1052852380264\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23905663a-154926339\right){x}-162458649312a-1052852380264$
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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.