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
9.2-a1
9.2-a
$2$
$2$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( - 3^{3} \)
$1.34929$
$(-a-4)$
0
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$29.55147182$
1.694893148
\( 1728 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 2 a + 32\) , \( 9 a + 29\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+32\right){x}+9a+29$
9.2-a2
9.2-a
$2$
$2$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( - 3^{3} \)
$1.34929$
$(-a-4)$
0
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$29.55147182$
1.694893148
\( 1728 \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 87 a + 381\) , \( 349 a + 1521\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(87a+381\right){x}+349a+1521$
9.2-b1
9.2-b
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{10} \)
$1.34929$
$(-a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$1.105793423$
$6.013673307$
3.051174382
\( -\frac{53248}{81} a - \frac{131072}{81} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( -4759 a + 20744\) , \( 231623 a - 1009626\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-4759a+20744\right){x}+231623a-1009626$
9.2-c1
9.2-c
$2$
$19$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{6} \)
$1.34929$
$(-a-4)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-19$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1.624922199$
$2.325972790$
1.734164921
\( -884736 \)
\( \bigl[0\) , \( 0\) , \( a\) , \( -16 a - 70\) , \( -73 a - 323\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-16a-70\right){x}-73a-323$
9.2-c2
9.2-c
$2$
$19$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{6} \)
$1.34929$
$(-a-4)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-19$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$0.085522221$
$44.19348301$
1.734164921
\( -884736 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -16 a - 70\) , \( 73 a + 318\bigr] \)
${y}^2+{y}={x}^{3}+\left(-16a-70\right){x}+73a+318$
9.2-d1
9.2-d
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{10} \)
$1.34929$
$(-a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.098423053$
$19.00729698$
0.858361815
\( -\frac{53248}{81} a - \frac{131072}{81} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -4759 a + 20744\) , \( -231623 a + 1009621\bigr] \)
${y}^2+{y}={x}^{3}+\left(-4759a+20744\right){x}-231623a+1009621$
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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.