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
49.1-b2
49.1-b
$4$
$6$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a-2), (-a+3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$9$
\( 2 \)
$1$
$24.30385482$
1.669195602
\( -\frac{1063343}{49} a + \frac{4416725}{49} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}+a+2$
343.1-d2
343.1-d
$4$
$6$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
343.1
\( 7^{3} \)
\( - 7^{9} \)
$2.79963$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$12.76327400$
1.753170515
\( -\frac{1063343}{49} a + \frac{4416725}{49} \)
\( \bigl[a\) , \( 1\) , \( 1\) , \( 20 a + 68\) , \( 236 a + 742\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(20a+68\right){x}+236a+742$
343.2-e2
343.2-e
$4$
$6$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
343.2
\( 7^{3} \)
\( - 7^{9} \)
$2.79963$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$4.822878717$
0.662473340
\( -\frac{1063343}{49} a + \frac{4416725}{49} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 3 a\) , \( -22\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+3a{x}-22$
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.