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
28.1-b1
28.1-b
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{4} \cdot 7^{4} \)
$1.49646$
$(-a-2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.095218482$
$22.21799898$
2.324760677
\( \frac{12774075}{9604} a - \frac{50451713}{9604} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -2 a\) , \( -a + 1\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-2a{x}-a+1$
196.2-a1
196.2-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
196.2
\( 2^{2} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{10} \)
$2.43411$
$(-a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$1$
$5.974754880$
3.282782799
\( \frac{12774075}{9604} a - \frac{50451713}{9604} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( 12 a + 42\) , \( -123 a - 388\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(12a+42\right){x}-123a-388$
1372.2-l1
1372.2-l
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1372.2
\( 2^{2} \cdot 7^{3} \)
\( 2^{4} \cdot 7^{10} \)
$3.95927$
$(-a-2), (-a+3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{3} \)
$1$
$2.859615246$
3.142386903
\( \frac{12774075}{9604} a - \frac{50451713}{9604} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 10 a - 3\) , \( 19 a - 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-3\right){x}+19a-6$
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.