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
242.4-a1
242.4-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.4
\( 2 \cdot 11^{2} \)
\( 2 \cdot 11^{8} \)
$0.93248$
$(-a+1), (-2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.1 , 11B.3.1
$1$
\( 3 \)
$1$
$2.651529103$
0.668122533
\( -\frac{263}{2} a + 453 \)
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -5\) , \( -6 a + 4\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}-5{x}-6a+4$
242.4-a2
242.4-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.4
\( 2 \cdot 11^{2} \)
\( 2^{33} \cdot 11^{4} \)
$0.93248$
$(-a+1), (-2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.2 , 11B.3.2
$1$
\( 1 \)
$1$
$0.883843034$
0.668122533
\( \frac{19838216722297}{8589934592} a - \frac{1095231860667}{4294967296} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 24 a - 73\) , \( 90 a - 232\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(24a-73\right){x}+90a-232$
242.4-a3
242.4-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.4
\( 2 \cdot 11^{2} \)
\( 2^{11} \cdot 11^{4} \)
$0.93248$
$(-a+1), (-2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.1 , 11B.3.2
$1$
\( 3 \)
$1$
$2.651529103$
0.668122533
\( \frac{14067329}{2048} a + \frac{51999917}{1024} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -11 a + 7\) , \( 7 a - 25\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+7\right){x}+7a-25$
242.4-a4
242.4-a
$4$
$33$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
242.4
\( 2 \cdot 11^{2} \)
\( 2^{3} \cdot 11^{8} \)
$0.93248$
$(-a+1), (-2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 11$
3B.1.2 , 11B.3.1
$1$
\( 1 \)
$1$
$0.883843034$
0.668122533
\( \frac{424896929}{8} a + \frac{349159757}{4} \)
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 95 a - 395\) , \( -1131 a + 2731\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(95a-395\right){x}-1131a+2731$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.