Elliptic curves over \(\Q(\sqrt{393}) \)

Results (4 matches)

 

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	$1$	$1$	\(\Q(\sqrt{393}) \)	$2$	$[2, 0]$	9.1	\( 3^{2} \)	\( 3^{9} \)	$3.06828$	$(-842a+8767)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$1$	$19.31615476$	1.948742231	\( -43563 a - 408459 \)	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -25675113778606 a + 267332206511615\) , \( 72944940012588806855 a - 759511016603567899154\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-25675113778606a+267332206511615\right){x}+72944940012588806855a-759511016603567899154$
9.1-b1	9.1-b	$1$	$1$	\(\Q(\sqrt{393}) \)	$2$	$[2, 0]$	9.1	\( 3^{2} \)	\( 3^{9} \)	$3.06828$	$(-842a+8767)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$1$	$4.828232283$	0.487104202	\( 43563 a - 452022 \)	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -2 a + 120\) , \( 129 a - 1138\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+120\right){x}+129a-1138$
9.1-c1	9.1-c	$1$	$1$	\(\Q(\sqrt{393}) \)	$2$	$[2, 0]$	9.1	\( 3^{2} \)	\( 3^{9} \)	$3.06828$	$(-842a+8767)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$1$	$19.31615476$	1.948742231	\( 43563 a - 452022 \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 25675113778604 a + 241657092733010\) , \( -72944940012588806856 a - 686566076590979092299\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(25675113778604a+241657092733010\right){x}-72944940012588806856a-686566076590979092299$
9.1-d1	9.1-d	$1$	$1$	\(\Q(\sqrt{393}) \)	$2$	$[2, 0]$	9.1	\( 3^{2} \)	\( 3^{9} \)	$3.06828$	$(-842a+8767)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$1$	$4.828232283$	0.487104202	\( -43563 a - 408459 \)	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( a + 118\) , \( -129 a - 1009\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+118\right){x}-129a-1009$

 

  *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.