Elliptic curves over Q(−2)\Q(\sqrt{-2}) of conductor 11552.2

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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
11552.2-a1	11552.2-a	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{6} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$2$	$0.071171000$	$5.963775842$	2.401039863	$\frac{27000}{19}$	$\bigl[a$ , $-1$ , $a$ , $3$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}$
11552.2-b1	11552.2-b	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓						$1$	$2$	$0.319679844$	$4.296507316$	3.884863868	$\frac{64}{19}$	$\bigl[0$ , $a$ , $0$ , $-1$ , $a\bigr]$	${y}^2={x}^{3}+a{x}^{2}-{x}+a$
11552.2-c1	11552.2-c	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{10}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$5$	5Ns	$1$	$2^{2} \cdot 5^{2}$	$0.029707001$	$0.603483608$	5.070716035	$-\frac{4741632}{2476099}$	$\bigl[0$ , $0$ , $0$ , $-14$ , $606\bigr]$	${y}^2={x}^{3}-14{x}+606$
11552.2-d1	11552.2-d	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$2^{2}$	$0.109359759$	$4.183446943$	5.176030150	$-\frac{13824}{19}$	$\bigl[0$ , $0$ , $0$ , $-2$ , $2\bigr]$	${y}^2={x}^{3}-2{x}+2$
11552.2-e1	11552.2-e	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$2$	$0.317256616$	$4.183446943$	3.753962649	$-\frac{13824}{19}$	$\bigl[0$ , $0$ , $0$ , $-2$ , $-2\bigr]$	${y}^2={x}^{3}-2{x}-2$
11552.2-f1	11552.2-f	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{10}$	$2.62028$	$(a), (-3a+1), (3a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$5$	5Ns	$1$	$2^{2}$	$1$	$0.603483608$	1.706909408	$-\frac{4741632}{2476099}$	$\bigl[0$ , $0$ , $0$ , $-14$ , $-606\bigr]$	${y}^2={x}^{3}-14{x}-606$
11552.2-g1	11552.2-g	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{12} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓						$1$	$2$	$0.319679844$	$4.296507316$	3.884863868	$\frac{64}{19}$	$\bigl[0$ , $-a$ , $0$ , $-1$ , $-a\bigr]$	${y}^2={x}^{3}-a{x}^{2}-{x}-a$
11552.2-h1	11552.2-h	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	11552.2	$2^{5} \cdot 19^{2}$	$2^{6} \cdot 19^{2}$	$2.62028$	$(a), (-3a+1), (3a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$2$	$1$	$5.963775842$	8.434052680	$\frac{27000}{19}$	$\bigl[a$ , $-1$ , $0$ , $2$ , $-1\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-1$

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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.