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
9.1-a1
9.1-a
$4$
$6$
5.5.36497.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( 3^{10} \)
$21.26627$
$(a^2-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$386.5609799$
1.01171790
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \)
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 106 a^{4} - 70 a^{3} - 413 a^{2} - 23 a + 81\) , \( 2837 a^{4} - 1889 a^{3} - 11031 a^{2} - 533 a + 2126\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){x}^{2}+\left(106a^{4}-70a^{3}-413a^{2}-23a+81\right){x}+2837a^{4}-1889a^{3}-11031a^{2}-533a+2126$
9.1-b1
9.1-b
$4$
$6$
5.5.36497.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( 3^{10} \)
$21.26627$
$(a^2-1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$3087.086684$
0.897734128
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \)
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + a - 1\) , \( 0\) , \( 2 a^{2} - a\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+a-1\right){x}^{2}+\left(2a^{2}-a\right){x}$
507.1-c1
507.1-c
$4$
$6$
5.5.36497.1
$5$
$[5, 0]$
507.1
\( 3 \cdot 13^{2} \)
\( 3^{4} \cdot 13^{6} \)
$31.82496$
$(a^2-1), (a^3-3a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.036783905$
$3451.926159$
3.32323271
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \)
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{2} - a - 2\) , \( -a^{4} + 10 a^{2} - 6 a - 6\) , \( -2 a^{3} + 4 a^{2} + 3 a\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-a^{4}+10a^{2}-6a-6\right){x}-2a^{3}+4a^{2}+3a$
507.1-p1
507.1-p
$4$
$6$
5.5.36497.1
$5$
$[5, 0]$
507.1
\( 3 \cdot 13^{2} \)
\( 3^{4} \cdot 13^{6} \)
$31.82496$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$189.2507428$
1.98124875
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \)
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( 3 a^{4} - 7 a^{3} - a^{2} + 12 a - 7\) , \( 5 a^{4} - 11 a^{3} - 7 a^{2} + 23 a - 8\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+8a+3\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(3a^{4}-7a^{3}-a^{2}+12a-7\right){x}+5a^{4}-11a^{3}-7a^{2}+23a-8$
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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.