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
539.1-a1
539.1-a
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{4} \cdot 11^{2} \)
$1.42801$
$(-2a+1), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cn
$1$
\( 2^{2} \)
$0.017231824$
$4.822573867$
0.801795807
\( \frac{884736}{539} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 2\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+2{x}$
539.1-b1
539.1-b
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{4} \cdot 11^{2} \)
$1.42801$
$(-2a+1), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.1
$4$
\( 2^{2} \)
$1$
$1.803987222$
1.933947068
\( -\frac{78843215872}{539} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$
539.1-b2
539.1-b
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{12} \cdot 11^{6} \)
$1.42801$
$(-2a+1), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3Cs.1.1
$4$
\( 2^{2} \cdot 3 \)
$1$
$0.601329074$
1.933947068
\( -\frac{13278380032}{156590819} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$
539.1-b3
539.1-b
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{4} \cdot 11^{18} \)
$1.42801$
$(-2a+1), (7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.2
$4$
\( 2^{2} \)
$1$
$0.200443024$
1.933947068
\( \frac{9463555063808}{115539436859} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$
539.1-c1
539.1-c
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{6} \cdot 11^{4} \)
$1.42801$
$(-2a+1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.295982175$
$2.375448597$
2.543876941
\( \frac{4657463}{41503} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}+11$
539.1-c2
539.1-c
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{12} \cdot 11^{2} \)
$1.42801$
$(-2a+1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.591964351$
$1.187724298$
2.543876941
\( \frac{15124197817}{1294139} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-51{x}+110$
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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.