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
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{9} \)
$0.53615$
$(a)$
0
$\Z/2\Z$
$\textsf{potential}$
$-36$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$3.283496869$
0.473931950
\( -44330496 a + 76771008 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 25 a - 45\) , \( 72 a - 127\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-45\right){x}+72a-127$
9.1-a2
9.1-a
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{9} \)
$0.53615$
$(a)$
0
$\Z/6\Z$
$\textsf{potential}$
$-36$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$29.55147182$
0.473931950
\( -44330496 a + 76771008 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 25 a - 45\) , \( -117 a + 202\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-45\right){x}-117a+202$
9.1-a3
9.1-a
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{3} \)
$0.53615$
$(a)$
0
$\Z/6\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \)
$1$
$29.55147182$
0.473931950
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}$
9.1-a4
9.1-a
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{3} \)
$0.53615$
$(a)$
0
$\Z/6\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \)
$1$
$29.55147182$
0.473931950
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a + 13\) , \( 6 a - 10\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+13\right){x}+6a-10$
9.1-a5
9.1-a
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{9} \)
$0.53615$
$(a)$
0
$\Z/2\Z$
$\textsf{potential}$
$-36$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$3.283496869$
0.473931950
\( 44330496 a + 76771008 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 88 a - 152\) , \( 564 a - 977\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(88a-152\right){x}+564a-977$
9.1-a6
9.1-a
$6$
$18$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{9} \)
$0.53615$
$(a)$
0
$\Z/6\Z$
$\textsf{potential}$
$-36$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$29.55147182$
0.473931950
\( 44330496 a + 76771008 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 88 a - 152\) , \( -717 a + 1242\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(88a-152\right){x}-717a+1242$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.