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-a5
28.1-a
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$0.94197$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$7.027708105$
1.533571636
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 52 a - 148\) , \( 346 a - 969\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(52a-148\right){x}+346a-969$
28.1-b5
28.1-b
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$0.94197$
$(a+3), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$35.33144352$
0.856661451
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
252.1-a5
252.1-a
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{2} \cdot 3^{6} \cdot 7^{4} \)
$1.63154$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.586035262$
$9.097601735$
2.326864094
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -32 a - 63\) , \( 147 a + 257\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-32a-63\right){x}+147a+257$
252.1-d5
252.1-d
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{2} \cdot 3^{6} \cdot 7^{4} \)
$1.63154$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.586035262$
$9.097601735$
2.326864094
\( \frac{128787625}{98} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 31 a - 95\) , \( -147 a + 404\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(31a-95\right){x}-147a+404$
1792.1-d5
1792.1-d
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{26} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$4$
\( 2^{3} \)
$1$
$1.756927026$
3.067143272
\( \frac{128787625}{98} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -784\bigr] \)
${y}^2={x}^{3}-{x}^{2}-168{x}-784$
1792.1-bp5
1792.1-bp
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{26} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.273389205$
$8.832860880$
4.215635879
\( \frac{128787625}{98} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 842 a - 2355\) , \( -19657 a + 54882\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(842a-2355\right){x}-19657a+54882$
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.