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
3.1-a4
3.1-a
$4$
$6$
3.3.1076.1
$3$
$[3, 0]$
3.1
\( 3 \)
\( - 3^{2} \)
$3.52018$
$(a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$90.59389658$
1.380901840
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \)
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 5\) , \( -2 a^{2} - 8 a - 7\) , \( -13 a^{2} - 44 a - 32\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a^{2}-8a-7\right){x}-13a^{2}-44a-32$
3.1-b3
3.1-b
$4$
$6$
3.3.1076.1
$3$
$[3, 0]$
3.1
\( 3 \)
\( - 3^{2} \)
$3.52018$
$(a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$0.099174988$
$273.3102172$
1.239490354
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \)
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 5\) , \( 346 a^{2} - 808 a - 895\) , \( 930 a^{2} - 2165 a - 2400\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(346a^{2}-808a-895\right){x}+930a^{2}-2165a-2400$
9.2-a1
9.2-a
$4$
$6$
3.3.1076.1
$3$
$[3, 0]$
9.2
\( 3^{2} \)
\( - 3^{8} \)
$4.22751$
$(a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$55.83346769$
1.702113303
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \)
\( \bigl[a^{2} - a - 4\) , \( a - 1\) , \( a + 1\) , \( a^{2} - 8 a - 7\) , \( -3 a^{2} - 11 a - 7\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}-8a-7\right){x}-3a^{2}-11a-7$
9.2-b1
9.2-b
$4$
$6$
3.3.1076.1
$3$
$[3, 0]$
9.2
\( 3^{2} \)
\( - 3^{8} \)
$4.22751$
$(a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$147.8219580$
0.500714658
\( \frac{21347776}{9} a^{2} + \frac{22397120}{3} a + \frac{40712752}{9} \)
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 17341 a^{2} - 40389 a - 44671\) , \( 224494 a^{2} - 522820 a - 578373\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(17341a^{2}-40389a-44671\right){x}+224494a^{2}-522820a-578373$
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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.