Elliptic curves over Q(−2)\Q(\sqrt{-2}) of conductor 9216.2

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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
9216.2-a1	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{3}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.504669137$	$1.360046576$	3.882715037	$-\frac{41803784}{9} a - \frac{21890312}{9}$	$\bigl[0$ , $-1$ , $0$ , $64 a - 63$ , $292 a - 37\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(64a-63\right){x}+292a-37$
9216.2-a2	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{3}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.504669137$	$1.360046576$	3.882715037	$\frac{41803784}{9} a - \frac{21890312}{9}$	$\bigl[0$ , $-1$ , $0$ , $-64 a - 63$ , $-292 a - 37\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-64a-63\right){x}-292a-37$
9216.2-a3	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{9}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.504669137$	$1.360046576$	3.882715037	$-\frac{27471928}{6561} a - \frac{56129704}{6561}$	$\bigl[0$ , $-1$ , $0$ , $24 a + 17$ , $-12 a - 101\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(24a+17\right){x}-12a-101$
9216.2-a4	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{9}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$0.504669137$	$1.360046576$	3.882715037	$\frac{27471928}{6561} a - \frac{56129704}{6561}$	$\bigl[0$ , $-1$ , $0$ , $-24 a + 17$ , $12 a - 101\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-24a+17\right){x}+12a-101$
9216.2-a5	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{6}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$0.504669137$	$2.720093152$	3.882715037	$-\frac{121088}{81} a - \frac{65728}{81}$	$\bigl[0$ , $-1$ , $0$ , $-4 a - 3$ , $-4 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-4a-3\right){x}-4a-1$
9216.2-a6	9216.2-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{6}$	$2.47639$	$(a), (-a-1), (a-1)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$0.504669137$	$2.720093152$	3.882715037	$\frac{121088}{81} a - \frac{65728}{81}$	$\bigl[0$ , $-1$ , $0$ , $4 a - 3$ , $4 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4a-3\right){x}+4a-1$
9216.2-b1	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{20}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 5$	2Cs, 5B	$1$	$2^{4}$	$2.833291884$	$0.687971971$	2.756621001	$-\frac{873722816}{59049}$	$\bigl[0$ , $-1$ , $0$ , $-159$ , $-765\bigr]$	${y}^2={x}^{3}-{x}^{2}-159{x}-765$
9216.2-b2	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{25}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2B, 5B	$1$	$2^{2}$	$5.666583769$	$0.343985985$	2.756621001	$-\frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401}$	$\bigl[0$ , $-1$ , $0$ , $220 a - 139$ , $-2304 a - 1593\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(220a-139\right){x}-2304a-1593$
9216.2-b3	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{25}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2B, 5B	$1$	$2^{2}$	$5.666583769$	$0.343985985$	2.756621001	$\frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401}$	$\bigl[0$ , $-1$ , $0$ , $-220 a - 139$ , $2304 a - 1593\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-220a-139\right){x}+2304a-1593$
9216.2-b4	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 5$	2Cs, 5B	$1$	$2^{4}$	$0.566658376$	$3.439859856$	2.756621001	$\frac{64}{9}$	$\bigl[0$ , $-1$ , $0$ , $1$ , $3\bigr]$	${y}^2={x}^{3}-{x}^{2}+{x}+3$
9216.2-b5	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{2}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 5$	2B, 5B	$1$	$2$	$1.133316753$	$3.439859856$	2.756621001	$\frac{85184}{3}$	$\bigl[0$ , $-1$ , $0$ , $-7$ , $-5\bigr]$	${y}^2={x}^{3}-{x}^{2}-7{x}-5$
9216.2-b6	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2B, 5B	$1$	$2^{2}$	$1.133316753$	$1.719929928$	2.756621001	$-\frac{2400472}{81} a + \frac{4984520}{81}$	$\bigl[0$ , $-1$ , $0$ , $20 a + 21$ , $-16 a + 71\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(20a+21\right){x}-16a+71$
9216.2-b7	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2B, 5B	$1$	$2^{2}$	$1.133316753$	$1.719929928$	2.756621001	$\frac{2400472}{81} a + \frac{4984520}{81}$	$\bigl[0$ , $-1$ , $0$ , $-20 a + 21$ , $16 a + 71\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-20a+21\right){x}+16a+71$
9216.2-b8	9216.2-b	$8$	$20$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{10}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 5$	2B, 5B	$1$	$2$	$5.666583769$	$0.687971971$	2.756621001	$\frac{58591911104}{243}$	$\bigl[0$ , $-1$ , $0$ , $-647$ , $6555\bigr]$	${y}^2={x}^{3}-{x}^{2}-647{x}+6555$
9216.2-c1	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{26} \cdot 3^{7}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$0.911404267$	1.288920275	$-\frac{18202756}{81} a - \frac{253086988}{81}$	$\bigl[0$ , $-1$ , $0$ , $-44 a + 213$ , $832 a + 455\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-44a+213\right){x}+832a+455$
9216.2-c2	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{26} \cdot 3^{7}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$0.911404267$	1.288920275	$\frac{18202756}{81} a - \frac{253086988}{81}$	$\bigl[0$ , $-1$ , $0$ , $44 a + 213$ , $-832 a + 455\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(44a+213\right){x}-832a+455$
9216.2-c3	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$3.645617069$	1.288920275	$-\frac{372736}{27} a - \frac{352256}{27}$	$\bigl[0$ , $-1$ , $0$ , $-4 a + 3$ , $2 a - 7\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-4a+3\right){x}+2a-7$
9216.2-c4	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$3.645617069$	1.288920275	$\frac{372736}{27} a - \frac{352256}{27}$	$\bigl[0$ , $-1$ , $0$ , $4 a + 3$ , $-2 a - 7\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4a+3\right){x}-2a-7$
9216.2-c5	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{22} \cdot 3^{8}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2^{4}$	$1$	$1.822808534$	1.288920275	$-\frac{855712}{729} a + \frac{467888}{729}$	$\bigl[0$ , $-1$ , $0$ , $4 a + 13$ , $-16 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4a+13\right){x}-16a-1$
9216.2-c6	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{22} \cdot 3^{8}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2^{4}$	$1$	$1.822808534$	1.288920275	$\frac{855712}{729} a + \frac{467888}{729}$	$\bigl[0$ , $-1$ , $0$ , $-4 a + 13$ , $16 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-4a+13\right){x}+16a-1$
9216.2-c7	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{26} \cdot 3^{13}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$0.911404267$	1.288920275	$-\frac{715706108}{531441} a + \frac{421307996}{531441}$	$\bigl[0$ , $-1$ , $0$ , $36 a - 27$ , $96 a + 87\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(36a-27\right){x}+96a+87$
9216.2-c8	9216.2-c	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{26} \cdot 3^{13}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$0.911404267$	1.288920275	$\frac{715706108}{531441} a + \frac{421307996}{531441}$	$\bigl[0$ , $-1$ , $0$ , $-36 a - 27$ , $-96 a + 87\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-36a-27\right){x}-96a+87$
9216.2-d1	9216.2-d	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{2}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.046050378$	$1.884597082$	2.787957272	$\frac{110584}{3} a - 1178880$	$\bigl[0$ , $-1$ , $0$ , $32 a + 1$ , $-68 a - 85\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(32a+1\right){x}-68a-85$
9216.2-d2	9216.2-d	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.046050378$	$1.884597082$	2.787957272	$-\frac{1862600}{81} a - \frac{2730832}{81}$	$\bigl[0$ , $-1$ , $0$ , $12 a + 21$ , $-24 a + 39\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(12a+21\right){x}-24a+39$
9216.2-d3	9216.2-d	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{16} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$0.523025189$	$3.769194165$	2.787957272	$640 a + \frac{6784}{9}$	$\bigl[0$ , $-1$ , $0$ , $2 a + 1$ , $-2 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(2a+1\right){x}-2a-1$
9216.2-d4	9216.2-d	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1.046050378$	$3.769194165$	2.787957272	$-\frac{109408}{81} a + \frac{158240}{81}$	$\bigl[0$ , $-1$ , $0$ , $-2 a - 2$ , $2 a + 2\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-2a-2\right){x}+2a+2$
9216.2-e1	9216.2-e	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{14}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$1.020976159$	1.443878331	$-\frac{105306568}{531441} a + \frac{136151936}{531441}$	$\bigl[0$ , $-1$ , $0$ , $-4 a - 27$ , $56 a - 73\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-4a-27\right){x}+56a-73$
9216.2-e2	9216.2-e	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{16} \cdot 3^{10}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$2.041952319$	1.443878331	$\frac{1668992}{729} a + \frac{3939968}{729}$	$\bigl[0$ , $-1$ , $0$ , $6 a + 13$ , $6 a - 21\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(6a+13\right){x}+6a-21$
9216.2-e3	9216.2-e	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{11}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$2.041952319$	1.443878331	$-\frac{24685856}{6561} a + \frac{51528992}{6561}$	$\bigl[0$ , $-1$ , $0$ , $4 a + 16$ , $14 a - 16\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4a+16\right){x}+14a-16$
9216.2-e4	9216.2-e	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	$2^{3}$	$1$	$1.020976159$	1.443878331	$\frac{576294904}{27} a + \frac{292647184}{27}$	$\bigl[0$ , $-1$ , $0$ , $96 a + 193$ , $564 a - 1173\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(96a+193\right){x}+564a-1173$
9216.2-f1	9216.2-f	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{14}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$1.020976159$	1.443878331	$\frac{105306568}{531441} a + \frac{136151936}{531441}$	$\bigl[0$ , $-1$ , $0$ , $4 a - 27$ , $-56 a - 73\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4a-27\right){x}-56a-73$
9216.2-f2	9216.2-f	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{16} \cdot 3^{10}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$2.041952319$	1.443878331	$-\frac{1668992}{729} a + \frac{3939968}{729}$	$\bigl[0$ , $-1$ , $0$ , $-6 a + 13$ , $-6 a - 21\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-6a+13\right){x}-6a-21$
9216.2-f3	9216.2-f	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{11}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$2.041952319$	1.443878331	$\frac{24685856}{6561} a + \frac{51528992}{6561}$	$\bigl[0$ , $-1$ , $0$ , $-4 a + 16$ , $-14 a - 16\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-4a+16\right){x}-14a-16$
9216.2-f4	9216.2-f	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	$2^{3}$	$1$	$1.020976159$	1.443878331	$-\frac{576294904}{27} a + \frac{292647184}{27}$	$\bigl[0$ , $-1$ , $0$ , $-96 a + 193$ , $-564 a - 1173\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-96a+193\right){x}-564a-1173$
9216.2-g1	9216.2-g	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{2}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.046050378$	$1.884597082$	2.787957272	$-\frac{110584}{3} a - 1178880$	$\bigl[0$ , $-1$ , $0$ , $-32 a + 1$ , $68 a - 85\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-32a+1\right){x}+68a-85$
9216.2-g2	9216.2-g	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.046050378$	$1.884597082$	2.787957272	$\frac{1862600}{81} a - \frac{2730832}{81}$	$\bigl[0$ , $-1$ , $0$ , $-12 a + 21$ , $24 a + 39\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-12a+21\right){x}+24a+39$
9216.2-g3	9216.2-g	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{16} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$0.523025189$	$3.769194165$	2.787957272	$-640 a + \frac{6784}{9}$	$\bigl[0$ , $-1$ , $0$ , $-2 a + 1$ , $2 a - 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-2a+1\right){x}+2a-1$
9216.2-g4	9216.2-g	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1.046050378$	$3.769194165$	2.787957272	$\frac{109408}{81} a + \frac{158240}{81}$	$\bigl[0$ , $-1$ , $0$ , $2 a - 2$ , $-2 a + 2\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(2a-2\right){x}-2a+2$
9216.2-h1	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{27} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$3.514366890$	$0.592819380$	2.946351043	$-\frac{15347957750}{81} a - \frac{35138997500}{81}$	$\bigl[0$ , $-1$ , $0$ , $-640 a + 257$ , $3060 a - 10437\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-640a+257\right){x}+3060a-10437$
9216.2-h2	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{27} \cdot 3^{5}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$3.514366890$	$0.592819380$	2.946351043	$\frac{15347957750}{81} a - \frac{35138997500}{81}$	$\bigl[0$ , $-1$ , $0$ , $640 a + 257$ , $-3060 a - 10437\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(640a+257\right){x}-3060a-10437$
9216.2-h3	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{8}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$0.878591722$	$2.371277522$	2.946351043	$-\frac{8000}{81}$	$\bigl[0$ , $-1$ , $0$ , $-3$ , $-9\bigr]$	${y}^2={x}^{3}-{x}^{2}-3{x}-9$
9216.2-h4	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{27} \cdot 3^{17}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$3.514366890$	$0.592819380$	2.946351043	$-\frac{56997401750}{43046721} a + \frac{87757407500}{43046721}$	$\bigl[0$ , $-1$ , $0$ , $80 a + 97$ , $-260 a + 443\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(80a+97\right){x}-260a+443$
9216.2-h5	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{27} \cdot 3^{17}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$3.514366890$	$0.592819380$	2.946351043	$\frac{56997401750}{43046721} a + \frac{87757407500}{43046721}$	$\bigl[0$ , $-1$ , $0$ , $-80 a + 97$ , $260 a + 443\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-80a+97\right){x}+260a+443$
9216.2-h6	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{10}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1.757183445$	$1.185638761$	2.946351043	$-\frac{100738000}{6561} a + \frac{45365000}{6561}$	$\bigl[0$ , $-1$ , $0$ , $-40 a + 17$ , $60 a - 165\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-40a+17\right){x}+60a-165$
9216.2-h7	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{24} \cdot 3^{10}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$1.757183445$	$1.185638761$	2.946351043	$\frac{100738000}{6561} a + \frac{45365000}{6561}$	$\bigl[0$ , $-1$ , $0$ , $40 a + 17$ , $-60 a - 165\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(40a+17\right){x}-60a-165$
9216.2-h8	9216.2-h	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{18} \cdot 3^{4}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$0.439295861$	$2.371277522$	2.946351043	$\frac{2744000}{9}$	$\bigl[0$ , $-1$ , $0$ , $-23$ , $51\bigr]$	${y}^2={x}^{3}-{x}^{2}-23{x}+51$
9216.2-i1	9216.2-i	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{14} \cdot 3^{3}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.845367848$	$3.155152462$	3.772081557	$-\frac{2820064}{9} a - \frac{1154272}{9}$	$\bigl[0$ , $a$ , $0$ , $8 a - 9$ , $-17 a - 2\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(8a-9\right){x}-17a-2$
9216.2-i2	9216.2-i	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{6}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$0.845367848$	$1.577576231$	3.772081557	$\frac{8113672}{81} a - \frac{1280704}{81}$	$\bigl[0$ , $a$ , $0$ , $12 a - 44$ , $-60 a + 96\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(12a-44\right){x}-60a+96$
9216.2-i3	9216.2-i	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{16} \cdot 3^{6}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{5}$	$0.422683924$	$3.155152462$	3.772081557	$-\frac{15232}{81} a + \frac{106112}{81}$	$\bigl[0$ , $a$ , $0$ , $2 a - 4$ , $0\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(2a-4\right){x}$
9216.2-i4	9216.2-i	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9216.2	$2^{10} \cdot 3^{2}$	$2^{23} \cdot 3^{9}$	$2.47639$	$(a), (-a-1), (a-1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$0.845367848$	$1.577576231$	3.772081557	$\frac{1905752}{6561} a + \frac{14345072}{6561}$	$\bigl[0$ , $a$ , $0$ , $-8 a + 16$ , $16 a + 16\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-8a+16\right){x}+16a+16$

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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.