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
8.1-a4
8.1-a
$6$
$8$
4.4.6224.1
$4$
$[4, 0]$
8.1
\( 2^{3} \)
\( - 2^{8} \)
$9.14239$
$(-a^3+a^2+4a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 2 \)
$1$
$14.12294371$
1.432123342
\( 1537921833441718305282 a^{3} - 2107454190479225749642 a^{2} - 6339631844534479587472 a + 5611518334448113253746 \)
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( -22 a^{3} + 41 a^{2} + 89 a - 122\) , \( -88 a^{3} + 144 a^{2} + 352 a - 423\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-22a^{3}+41a^{2}+89a-122\right){x}-88a^{3}+144a^{2}+352a-423$
8.1-b2
8.1-b
$6$
$8$
4.4.6224.1
$4$
$[4, 0]$
8.1
\( 2^{3} \)
\( - 2^{8} \)
$9.14239$
$(-a^3+a^2+4a-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$3.969775957$
$8.182282215$
1.646894014
\( 1537921833441718305282 a^{3} - 2107454190479225749642 a^{2} - 6339631844534479587472 a + 5611518334448113253746 \)
\( \bigl[a^{2} - a - 2\) , \( 1\) , \( a^{2} - 3\) , \( 11 a^{3} + 17 a^{2} - 38 a - 56\) , \( 62 a^{3} + 93 a^{2} - 192 a - 280\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(11a^{3}+17a^{2}-38a-56\right){x}+62a^{3}+93a^{2}-192a-280$
256.1-e3
256.1-e
$6$
$8$
4.4.6224.1
$4$
$[4, 0]$
256.1
\( 2^{8} \)
\( - 2^{20} \)
$14.09949$
$(-a^3+a^2+4a-2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$143.6375039$
0.910338817
\( 1537921833441718305282 a^{3} - 2107454190479225749642 a^{2} - 6339631844534479587472 a + 5611518334448113253746 \)
\( \bigl[a^{3} - 5 a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 3\) , \( 24 a^{3} + 26 a^{2} + 8 a - 23\) , \( -337 a^{3} - 222 a^{2} + 313 a + 73\bigr] \)
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(24a^{3}+26a^{2}+8a-23\right){x}-337a^{3}-222a^{2}+313a+73$
256.1-k4
256.1-k
$6$
$8$
4.4.6224.1
$4$
$[4, 0]$
256.1
\( 2^{8} \)
\( - 2^{20} \)
$14.09949$
$(-a^3+a^2+4a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$83.21796200$
2.109659081
\( 1537921833441718305282 a^{3} - 2107454190479225749642 a^{2} - 6339631844534479587472 a + 5611518334448113253746 \)
\( \bigl[a^{3} - 5 a\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 251 a^{3} - 471 a^{2} - 621 a + 663\) , \( 8201 a^{3} - 15355 a^{2} - 20459 a + 21906\bigr] \)
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(251a^{3}-471a^{2}-621a+663\right){x}+8201a^{3}-15355a^{2}-20459a+21906$
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Pari/GP
SageMath
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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.