Elliptic curves over \(\Q(\sqrt{-321}) \)

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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
8.1-a1	8.1-a	$1$	$1$	\(\Q(\sqrt{-321}) \)	$2$	$[0, 1]$	8.1	\( 2^{3} \)	\( 2^{20} \)	$5.38510$	$(2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓			$1$	\( 2 \)	$3.272510852$	$12.71369191$	9.288813722	\( 186624 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -95\) , \( 7 a\bigr] \)	${y}^2={x}^3-a{x}^2-95{x}+7a$
8.1-b1	8.1-b	$1$	$1$	\(\Q(\sqrt{-321}) \)	$2$	$[0, 1]$	8.1	\( 2^{3} \)	\( 2^{20} \)	$5.38510$	$(2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓			$1$	\( 2 \)	$3.272510852$	$12.71369191$	9.288813722	\( 186624 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -95\) , \( -7 a\bigr] \)	${y}^2={x}^3+a{x}^2-95{x}-7a$
8.1-c1	8.1-c	$1$	$1$	\(\Q(\sqrt{-321}) \)	$2$	$[0, 1]$	8.1	\( 2^{3} \)	\( 2^{8} \cdot 67^{12} \)	$5.38510$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓			$1$	\( 2^{2} \)	$2.846353727$	$12.71369191$	8.079193854	\( 186624 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -720 a - 3974\) , \( 30108 a - 127437\bigr] \)	${y}^2={x}^3+a{x}^2+\left(-720a-3974\right){x}+30108a-127437$
8.1-d1	8.1-d	$1$	$1$	\(\Q(\sqrt{-321}) \)	$2$	$[0, 1]$	8.1	\( 2^{3} \)	\( 2^{8} \cdot 67^{12} \)	$5.38510$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓			$1$	\( 2^{2} \)	$2.846353727$	$12.71369191$	8.079193854	\( 186624 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -720 a - 3974\) , \( -30108 a + 127437\bigr] \)	${y}^2={x}^3-a{x}^2+\left(-720a-3974\right){x}-30108a+127437$

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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.