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
114.1-a1
114.1-a
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
114.1
\( 2 \cdot 3 \cdot 19 \)
\( 2^{2} \cdot 3^{6} \cdot 19^{2} \)
$0.82587$
$(a), (-a-1), (-3a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.270868610$
1.156426687
\( \frac{1077927928}{263169} a - \frac{68584734209}{526338} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -a + 10\) , \( 6 a + 2\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+10\right){x}+6a+2$
114.1-a2
114.1-a
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
114.1
\( 2 \cdot 3 \cdot 19 \)
\( 2 \cdot 3^{12} \cdot 19^{4} \)
$0.82587$
$(a), (-a-1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.635434305$
1.156426687
\( \frac{15293908911617}{138515845122} a + \frac{38969351275232}{69257922561} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( 4 a + 10\) , \( 7 a + 24\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4a+10\right){x}+7a+24$
114.1-a3
114.1-a
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
114.1
\( 2 \cdot 3 \cdot 19 \)
\( 2^{4} \cdot 3^{3} \cdot 19 \)
$0.82587$
$(a), (-a-1), (-3a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.541737221$
1.156426687
\( -\frac{61816}{513} a + \frac{1231777}{2052} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$
114.1-a4
114.1-a
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
114.1
\( 2 \cdot 3 \cdot 19 \)
\( 2 \cdot 3^{3} \cdot 19 \)
$0.82587$
$(a), (-a-1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$1.635434305$
1.156426687
\( -\frac{1101457391617}{1026} a + \frac{8792832344816}{513} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -6 a + 170\) , \( 549 a + 68\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+170\right){x}+549a+68$
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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.