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-a5
21.1-a
$6$
$8$
4.4.9909.1
$4$
$[4, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{8} \cdot 7^{4} \)
$13.01460$
$(-a^3+a^2+4a), (a^3-a^2-4a+1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1.064084331$
$87.10503032$
3.724468981
\( -\frac{25780022}{21609} a^{3} - \frac{18946955}{21609} a^{2} + \frac{5547721}{2401} a - \frac{16556678}{21609} \)
\( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -50 a^{3} + 60 a^{2} + 227 a - 123\) , \( 382 a^{3} - 462 a^{2} - 1736 a + 949\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(-50a^{3}+60a^{2}+227a-123\right){x}+382a^{3}-462a^{2}-1736a+949$
21.1-d5
21.1-d
$6$
$8$
4.4.9909.1
$4$
$[4, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{8} \cdot 7^{4} \)
$13.01460$
$(-a^3+a^2+4a), (a^3-a^2-4a+1)$
$1$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$0.827279726$
$353.3517645$
2.936599577
\( -\frac{25780022}{21609} a^{3} - \frac{18946955}{21609} a^{2} + \frac{5547721}{2401} a - \frac{16556678}{21609} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( a + 1\) , \( a^{3} - 4 a^{2} - 6 a + 6\) , \( a^{2} - a - 1\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(a^{3}-4a^{2}-6a+6\right){x}+a^{2}-a-1$
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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.