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
242.3-a1
242.3-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.3
\( 2 \cdot 11^{2} \)
\( 2 \cdot 11^{8} \)
$0.93248$
$(a), (2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.1 , 11B.3.1
$1$
\( 3 \)
$1$
$2.651529103$
0.668122533
\( \frac{263}{2} a + \frac{643}{2} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a - 5\) , \( a + 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-5\right){x}+a+3$
242.3-a2
242.3-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.3
\( 2 \cdot 11^{2} \)
\( 2^{33} \cdot 11^{4} \)
$0.93248$
$(a), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.2 , 11B.3.2
$1$
\( 1 \)
$1$
$0.883843034$
0.668122533
\( -\frac{19838216722297}{8589934592} a + \frac{17647753000963}{8589934592} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -25 a - 49\) , \( -90 a - 142\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-25a-49\right){x}-90a-142$
242.3-a3
242.3-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.3
\( 2 \cdot 11^{2} \)
\( 2^{11} \cdot 11^{4} \)
$0.93248$
$(a), (2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.1 , 11B.3.2
$1$
\( 3 \)
$1$
$2.651529103$
0.668122533
\( -\frac{14067329}{2048} a + \frac{118067163}{2048} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 4\) , \( -7 a - 18\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(10a-4\right){x}-7a-18$
242.3-a4
242.3-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.3
\( 2 \cdot 11^{2} \)
\( 2^{3} \cdot 11^{8} \)
$0.93248$
$(a), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.2 , 11B.3.1
$1$
\( 1 \)
$1$
$0.883843034$
0.668122533
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -96 a - 300\) , \( 831 a + 2090\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-96a-300\right){x}+831a+2090$
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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.