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-d3
448.1-d
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{20} \cdot 7^{4} \)
$1.88394$
$(a+3), (2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$2.588244403$
$12.23735606$
3.455836897
\( \frac{740772}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \)
${y}^2={x}^{3}-19{x}+30$
448.1-e3
448.1-e
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
448.1
\( 2^{6} \cdot 7 \)
\( 2^{20} \cdot 7^{4} \)
$1.88394$
$(a+3), (2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$3.783918005$
$5.272587057$
2.176836612
\( \frac{740772}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 95 a - 266\) , \( 720 a - 2010\bigr] \)
${y}^2={x}^{3}+\left(95a-266\right){x}+720a-2010$
1792.1-b3
1792.1-b
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{20} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.568914384$
$12.23735606$
3.038469349
\( \frac{740772}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 95 a - 266\) , \( -720 a + 2010\bigr] \)
${y}^2={x}^{3}+\left(95a-266\right){x}-720a+2010$
1792.1-bm3
1792.1-bm
$4$
$4$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{20} \cdot 7^{4} \)
$2.66430$
$(a+3), (2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$2.235676329$
$5.272587057$
5.144616855
\( \frac{740772}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( -30\bigr] \)
${y}^2={x}^{3}-19{x}-30$
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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.