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
8.2-b1
8.2-b
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
8.2
\( 2^{3} \)
\( - 2^{10} \)
$3.42141$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$90.98749573$
1.680349917
\( -1723 a^{2} + 4372 a + 1724 \)
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( 9 a^{2} + 2 a - 67\) , \( -8 a^{2} - 2 a + 50\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(9a^{2}+2a-67\right){x}-8a^{2}-2a+50$
16.3-e1
16.3-e
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
16.3
\( 2^{4} \)
\( - 2^{10} \)
$3.84041$
$(a^2-6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.096242457$
$291.2841083$
1.553183502
\( -1723 a^{2} + 4372 a + 1724 \)
\( \bigl[a^{2} + a - 4\) , \( 1\) , \( a\) , \( -5 a^{2} + 26 a - 24\) , \( 29 a^{2} - 99 a + 76\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a^{2}+26a-24\right){x}+29a^{2}-99a+76$
64.4-b2
64.4-b
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
64.4
\( 2^{6} \)
\( - 2^{16} \)
$4.83861$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$166.6796878$
3.078227371
\( -1723 a^{2} + 4372 a + 1724 \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( a^{2} + a - 9\) , \( a^{2} - 7\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}+a-9\right){x}+a^{2}-7$
64.4-m1
64.4-m
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
64.4
\( 2^{6} \)
\( - 2^{16} \)
$4.83861$
$(a^2-6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.221163368$
$52.06520696$
1.275939441
\( -1723 a^{2} + 4372 a + 1724 \)
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a^{2} + a - 4\) , \( -2 a^{2} + 3 a\) , \( -5 a^{2} + 15 a - 12\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-2a^{2}+3a\right){x}-5a^{2}+15a-12$
200.4-c1
200.4-c
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
200.4
\( 2^{3} \cdot 5^{2} \)
\( - 2^{10} \cdot 5^{6} \)
$5.85053$
$(a^2-6), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$99.67173486$
3.681459526
\( -1723 a^{2} + 4372 a + 1724 \)
\( \bigl[a^{2} + a - 4\) , \( 0\) , \( 0\) , \( 7 a^{2} + 4 a - 43\) , \( 11 a^{2} + 3 a - 70\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(7a^{2}+4a-43\right){x}+11a^{2}+3a-70$
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Pari/GP
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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.