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
448.1-d4
448.1-d
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{22} \cdot 7^{2} \)
$1.88394$
$(a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1.294122201$
$12.23735606$
3.455836897
\( \frac{1443468546}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \)
${y}^2={x}^{3}-299{x}+1990$
448.1-e4
448.1-e
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{22} \cdot 7^{2} \)
$1.88394$
$(a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$7.567836011$
$1.318146764$
2.176836612
\( \frac{1443468546}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1495 a - 4186\) , \( 47760 a - 133330\bigr] \)
${y}^2={x}^{3}+\left(1495a-4186\right){x}+47760a-133330$
1792.1-b4
1792.1-b
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{22} \cdot 7^{2} \)
$2.66430$
$(a+3), (2)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1.137828769$
$12.23735606$
3.038469349
\( \frac{1443468546}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1495 a - 4186\) , \( -47760 a + 133330\bigr] \)
${y}^2={x}^{3}+\left(1495a-4186\right){x}-47760a+133330$
1792.1-bm4
1792.1-bm
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{22} \cdot 7^{2} \)
$2.66430$
$(a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$4.471352659$
$1.318146764$
5.144616855
\( \frac{1443468546}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( -1990\bigr] \)
${y}^2={x}^{3}-299{x}-1990$
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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.