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-a2
448.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{22} \cdot 7^{4} \)
$1.88394$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$11.37856052$
2.483005471
\( \frac{3543122}{49} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 202 a - 563\) , \( -2217 a + 6190\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(202a-563\right){x}-2217a+6190$
448.1-h2
448.1-h
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{22} \cdot 7^{4} \)
$1.88394$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.594960974$
0.784484799
\( \frac{3543122}{49} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \)
${y}^2={x}^{3}-{x}^{2}-40{x}-84$
1792.1-u2
1792.1-u
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{22} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$3.594960974$
6.275878394
\( \frac{3543122}{49} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 202 a - 563\) , \( 2217 a - 6190\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(202a-563\right){x}+2217a-6190$
1792.1-y2
1792.1-y
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{22} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.123099950$
$11.37856052$
2.445262812
\( \frac{3543122}{49} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -40\) , \( 84\bigr] \)
${y}^2={x}^{3}+{x}^{2}-40{x}+84$
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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.