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
49.3-a1
49.3-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{13} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.599378634$
$7.481352100$
2.463788418
\( \frac{1840001024}{823543} a + \frac{5775437824}{823543} \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( -4\) , \( -18 a + 70\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}-4{x}-18a+70$
49.3-a2
49.3-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{7} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.3
$1$
\( 2 \)
$4.195650442$
$1.068764585$
2.463788418
\( \frac{195338235078135808}{7} a - \frac{808691822475743232}{7} \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 7700 a - 37314\) , \( -834775 a + 3292065\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7700a-37314\right){x}-834775a+3292065$
49.3-b1
49.3-b
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \)
$0.214508932$
$18.74863282$
2.209718956
\( 4096 a + 12288 \)
\( \bigl[0\) , \( -1\) , \( a\) , \( 2 a - 8\) , \( 5 a - 25\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(2a-8\right){x}+5a-25$
49.3-b2
49.3-b
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{9} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \)
$1.501562525$
$2.678376117$
2.209718956
\( 68910804992 a + 216383696896 \)
\( \bigl[0\) , \( -1\) , \( a\) , \( 232 a - 978\) , \( -3994 a + 16508\bigr] \)
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(232a-978\right){x}-3994a+16508$
49.3-c1
49.3-c
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{9} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.2.1
$1$
\( 2 \)
$0.233677833$
$15.92365378$
2.044477338
\( 4096 a + 12288 \)
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -25 a - 73\) , \( 98 a + 303\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-73\right){x}+98a+303$
49.3-c2
49.3-c
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.2.3
$1$
\( 2 \)
$1.635744836$
$2.274807683$
2.044477338
\( 68910804992 a + 216383696896 \)
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 4 a - 27\) , \( 24 a - 110\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-27\right){x}+24a-110$
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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.