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-a4
21.1-a
$4$
$6$
4.4.19821.1
$4$
$[4, 0]$
21.1
\( 3 \cdot 7 \)
\( - 3^{12} \cdot 7^{2} \)
$18.40682$
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \cdot 3 \)
$1$
$77.08983698$
3.285379908
\( -\frac{841064654581664}{35721} a^{3} + \frac{1030023415263169}{11907} a^{2} - \frac{511441919731475}{11907} a - \frac{943603335173858}{35721} \)
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -19 a^{3} - 3 a^{2} + 150 a + 54\) , \( 148 a^{3} + 16 a^{2} - 1167 a - 407\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-19a^{3}-3a^{2}+150a+54\right){x}+148a^{3}+16a^{2}-1167a-407$
63.1-c4
63.1-c
$4$
$6$
4.4.19821.1
$4$
$[4, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( - 3^{18} \cdot 7^{2} \)
$21.11635$
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.220824500$
$196.7622796$
2.468972820
\( -\frac{841064654581664}{35721} a^{3} + \frac{1030023415263169}{11907} a^{2} - \frac{511441919731475}{11907} a - \frac{943603335173858}{35721} \)
\( \bigl[1\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( 1\) , \( -12 a^{3} - 2 a^{2} + 92 a + 31\) , \( \frac{268}{3} a^{3} + \frac{34}{3} a^{2} - 700 a - 245\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+1\right){x}^{2}+\left(-12a^{3}-2a^{2}+92a+31\right){x}+\frac{268}{3}a^{3}+\frac{34}{3}a^{2}-700a-245$
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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.