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
21.1-a6
21.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{4} \)
$0.87660$
$(-a+2), (a+3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$14.60752776$
0.796905972
\( \frac{53297461115137}{147} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 3920 a - 10977\) , \( -200440 a + 559528\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3920a-10977\right){x}-200440a+559528$
21.1-b6
21.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{4} \)
$0.87660$
$(-a+2), (a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.638508823$
$0.814020435$
0.937376813
\( \frac{53297461115137}{147} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)
${y}^2+{x}{y}={x}^{3}-784{x}-8515$
63.1-a6
63.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{8} \cdot 7^{4} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.990881389$
1.737783746
\( \frac{53297461115137}{147} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 2352 a - 7056\) , \( 102180 a - 280995\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2352a-7056\right){x}+102180a-280995$
63.1-b6
63.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{8} \cdot 7^{4} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.990881389$
1.737783746
\( \frac{53297461115137}{147} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2352 a - 4704\) , \( -102180 a - 178815\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-2352a-4704\right){x}-102180a-178815$
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.