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-b2
8.2-b
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
8.2
\( 2^{3} \)
\( 2^{8} \)
$3.42141$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$45.49374786$
1.680349917
\( 26933208 a^{2} - 99554907 a + 79908472 \)
\( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( -2 a^{2} + 10 a - 7\) , \( -13 a^{2} + 55 a - 50\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}+10a-7\right){x}-13a^{2}+55a-50$
16.3-e2
16.3-e
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
16.3
\( 2^{4} \)
\( 2^{8} \)
$3.84041$
$(a^2-6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.192484915$
$145.6420541$
1.553183502
\( 26933208 a^{2} - 99554907 a + 79908472 \)
\( \bigl[a\) , \( 1\) , \( a^{2} + a - 4\) , \( -41 a^{2} + 148 a - 116\) , \( 406 a^{2} - 1504 a + 1208\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+{x}^{2}+\left(-41a^{2}+148a-116\right){x}+406a^{2}-1504a+1208$
64.4-b1
64.4-b
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
64.4
\( 2^{6} \)
\( 2^{14} \)
$4.83861$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$83.33984394$
3.078227371
\( 26933208 a^{2} - 99554907 a + 79908472 \)
\( \bigl[a^{2} - 4\) , \( a\) , \( a^{2} - 4\) , \( 7 a^{2} + 15 a - 28\) , \( 15 a^{2} + 19 a - 44\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(7a^{2}+15a-28\right){x}+15a^{2}+19a-44$
64.4-m2
64.4-m
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
64.4
\( 2^{6} \)
\( 2^{14} \)
$4.83861$
$(a^2-6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.442326736$
$26.03260348$
1.275939441
\( 26933208 a^{2} - 99554907 a + 79908472 \)
\( \bigl[a^{2} + a - 4\) , \( 0\) , \( a^{2} - 4\) , \( 10 a^{2} + 58 a - 84\) , \( 9 a^{2} + 229 a - 284\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(10a^{2}+58a-84\right){x}+9a^{2}+229a-284$
200.4-c2
200.4-c
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
200.4
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{6} \)
$5.85053$
$(a^2-6), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$49.83586743$
3.681459526
\( 26933208 a^{2} - 99554907 a + 79908472 \)
\( \bigl[a\) , \( a^{2} - a - 5\) , \( 0\) , \( 5 a^{2} + 10 a - 12\) , \( -2 a^{2} - 4 a + 4\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(5a^{2}+10a-12\right){x}-2a^{2}-4a+4$
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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.