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
9.3-a2
9.3-a
$4$
$6$
\(\Q(\sqrt{3}, \sqrt{7})\)
$4$
$[4, 0]$
9.3
\( 3^{2} \)
\( 3^{10} \)
$9.87866$
$(-a-1), (-a^3+5a-1)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$0.077414024$
$1179.984011$
1.449957322
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \)
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( 1\) , \( -22 a^{3} + 11 a^{2} + 106 a - 47\) , \( 98 a^{3} - 43 a^{2} - 467 a + 213\bigr] \)
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-22a^{3}+11a^{2}+106a-47\right){x}+98a^{3}-43a^{2}-467a+213$
9.3-b4
9.3-b
$4$
$6$
\(\Q(\sqrt{3}, \sqrt{7})\)
$4$
$[4, 0]$
9.3
\( 3^{2} \)
\( 3^{10} \)
$9.87866$
$(-a-1), (-a^3+5a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$0.116121037$
$131.1093345$
1.449957322
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \)
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -20 a^{3} + 10 a^{2} + 96 a - 47\) , \( -118 a^{3} + 54 a^{2} + 564 a - 263\bigr] \)
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-20a^{3}+10a^{2}+96a-47\right){x}-118a^{3}+54a^{2}+564a-263$
81.1-a1
81.1-a
$4$
$6$
\(\Q(\sqrt{3}, \sqrt{7})\)
$4$
$[4, 0]$
81.1
\( 3^{4} \)
\( 3^{22} \)
$13.00105$
$(-a-1), (-a^3+5a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$131.1093345$
3.121650822
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \)
\( \bigl[a^{3} - 4 a + 1\) , \( -1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -11 a^{3} + 12 a^{2} + 64 a - 32\) , \( -28 a^{3} + 56 a^{2} + 207 a - 110\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}-{x}^{2}+\left(-11a^{3}+12a^{2}+64a-32\right){x}-28a^{3}+56a^{2}+207a-110$
81.1-j3
81.1-j
$4$
$6$
\(\Q(\sqrt{3}, \sqrt{7})\)
$4$
$[4, 0]$
81.1
\( 3^{4} \)
\( 3^{22} \)
$13.00105$
$(-a-1), (-a^3+5a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$131.1093345$
3.121650822
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \)
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a - 1\) , \( a^{2} + a - 2\) , \( -11 a^{3} + 11 a^{2} + 63 a - 30\) , \( 29 a^{3} - 56 a^{2} - 213 a + 106\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(-11a^{3}+11a^{2}+63a-30\right){x}+29a^{3}-56a^{2}-213a+106$
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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.