Elliptic curves over Q(2)\Q(\sqrt{2}) of conductor 784.1

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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
784.1-a1	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{48} \cdot 7^{2}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$3.513854052$	1.242335014	$-\frac{548347731625}{1835008}$	$\bigl[a$ , $-1$ , $0$ , $-682$ , $6990\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-682{x}+6990$
784.1-a2	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{16} \cdot 7^{2}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$3.513854052$	1.242335014	$-\frac{15625}{28}$	$\bigl[a$ , $-1$ , $0$ , $-2$ , $-2\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}-2$
784.1-a3	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{24} \cdot 7^{6}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3Cs	$1$	$2^{2}$	$1$	$3.513854052$	1.242335014	$\frac{9938375}{21952}$	$\bigl[a$ , $-1$ , $0$ , $18$ , $46\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}+46$
784.1-a4	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{13} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$-\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401}$	$\bigl[a$ , $-1$ , $0$ , $220 a - 362$ , $2320 a - 3330\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(220a-362\right){x}+2320a-3330$
784.1-a5	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{18} \cdot 7^{12}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3Cs	$1$	$2^{4}$	$1$	$3.513854052$	1.242335014	$\frac{4956477625}{941192}$	$\bigl[a$ , $-1$ , $0$ , $-142$ , $558\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-142{x}+558$
784.1-a6	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{15} \cdot 7^{15}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$-\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201}$	$\bigl[a$ , $-1$ , $0$ , $520 a - 1422$ , $-16000 a + 16302\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(520a-1422\right){x}-16000a+16302$
784.1-a7	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{21} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$-\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401}$	$\bigl[a$ , $-1$ , $0$ , $57920 a - 92842$ , $-9795840 a + 14293838\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(57920a-92842\right){x}-9795840a+14293838$
784.1-a8	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{14} \cdot 7^{4}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2^{4}$	$1$	$3.513854052$	1.242335014	$\frac{128787625}{98}$	$\bigl[a$ , $-1$ , $0$ , $-42$ , $-98\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-42{x}-98$
784.1-a9	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{15} \cdot 7^{15}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201}$	$\bigl[a$ , $-1$ , $0$ , $-520 a - 1422$ , $16000 a + 16302\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-520a-1422\right){x}+16000a+16302$
784.1-a10	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{30} \cdot 7^{4}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2^{4}$	$1$	$3.513854052$	1.242335014	$\frac{2251439055699625}{25088}$	$\bigl[a$ , $-1$ , $0$ , $-10922$ , $441166\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-10922{x}+441166$
784.1-a11	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{13} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401}$	$\bigl[a$ , $-1$ , $0$ , $-220 a - 362$ , $-2320 a - 3330\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-220a-362\right){x}-2320a-3330$
784.1-a12	784.1-a	$12$	$36$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{21} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$1.756927026$	1.242335014	$\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401}$	$\bigl[a$ , $-1$ , $0$ , $-57920 a - 92842$ , $9795840 a + 14293838\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-57920a-92842\right){x}+9795840a+14293838$
784.1-b1	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{10} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$8.330553587$	1.472647733	$-\frac{69495892205440052}{49} a + \frac{98282033286152638}{49}$	$\bigl[a$ , $a - 1$ , $0$ , $115 a - 122$ , $-322 a + 1587\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(115a-122\right){x}-322a+1587$
784.1-b2	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{8} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$4.165276793$	1.472647733	$-\frac{13282665232}{5764801} a + \frac{23566456972}{5764801}$	$\bigl[a$ , $a - 1$ , $0$ , $15 a + 18$ , $-30 a - 43\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+18\right){x}-30a-43$
784.1-b3	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{4} \cdot 7^{6}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2}$	$1$	$16.66110717$	1.472647733	$-\frac{4566144}{2401} a + \frac{14497232}{2401}$	$\bigl[a$ , $a - 1$ , $0$ , $-5 a - 7$ , $-7 a - 9\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-7\right){x}-7a-9$
784.1-b4	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{8} \cdot 7^{6}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$16.66110717$	1.472647733	$-\frac{53744933616}{2401} a + \frac{76065896132}{2401}$	$\bigl[a$ , $a - 1$ , $0$ , $-25 a - 52$ , $84 a + 159\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-52\right){x}+84a+159$
784.1-b5	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{8} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$8.330553587$	1.472647733	$\frac{110288896}{49} a + \frac{155981824}{49}$	$\bigl[0$ , $-a + 1$ , $0$ , $-6 a + 7$ , $-23 a + 32\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+7\right){x}-23a+32$
784.1-b6	784.1-b	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{10} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$1$	$8.330553587$	1.472647733	$\frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801}$	$\bigl[a$ , $a$ , $0$ , $194 a - 314$ , $-2200 a + 3186\bigr]$	${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(194a-314\right){x}-2200a+3186$
784.1-c1	784.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{8} \cdot 7^{2}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$0.239919898$	$22.75712104$	1.930361270	$-\frac{4}{7}$	$\bigl[a$ , $0$ , $a$ , $-1$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}$
784.1-c2	784.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{11} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$0.239919898$	$11.37856052$	1.930361270	$-\frac{4347206325605}{2401} a + \frac{6147883179496}{2401}$	$\bigl[a$ , $0$ , $a$ , $50 a - 91$ , $-274 a + 370\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(50a-91\right){x}-274a+370$
784.1-c3	784.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{10} \cdot 7^{4}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$0.119959949$	$22.75712104$	1.930361270	$\frac{3543122}{49}$	$\bigl[a$ , $0$ , $a$ , $-11$ , $10\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-11{x}+10$
784.1-c4	784.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{11} \cdot 7^{5}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$0.239919898$	$11.37856052$	1.930361270	$\frac{4347206325605}{2401} a + \frac{6147883179496}{2401}$	$\bigl[a$ , $0$ , $a$ , $-50 a - 91$ , $274 a + 370\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-50a-91\right){x}+274a+370$
784.1-d1	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{4} \cdot 7^{2}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$1$	$1.069108576$	$10.54517411$	1.992969164	$\frac{432}{7}$	$\bigl[a$ , $1$ , $0$ , $1$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}$
784.1-d2	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{11} \cdot 7^{10}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{6}$	$0.133638572$	$5.272587057$	1.992969164	$-\frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801}$	$\bigl[a$ , $1$ , $0$ , $90 a - 94$ , $-368 a + 642\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(90a-94\right){x}-368a+642$
784.1-d3	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{10} \cdot 7^{8}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$0.267277144$	$10.54517411$	1.992969164	$\frac{11090466}{2401}$	$\bigl[a$ , $1$ , $0$ , $-14$ , $10\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}-14{x}+10$
784.1-d4	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{8} \cdot 7^{4}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.534554288$	$10.54517411$	1.992969164	$\frac{740772}{49}$	$\bigl[a$ , $1$ , $0$ , $-4$ , $-6\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}-6$
784.1-d5	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{11} \cdot 7^{10}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{6}$	$0.133638572$	$5.272587057$	1.992969164	$\frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801}$	$\bigl[a$ , $1$ , $0$ , $-90 a - 94$ , $368 a + 642\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-90a-94\right){x}+368a+642$
784.1-d6	784.1-d	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{10} \cdot 7^{2}$	$1.33740$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1.069108576$	$2.636293528$	1.992969164	$\frac{1443468546}{7}$	$\bigl[a$ , $1$ , $0$ , $-74$ , $-286\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}-74{x}-286$
784.1-e1	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{10} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$1$	$8.330553587$	1.472647733	$-\frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801}$	$\bigl[a$ , $-a$ , $0$ , $-194 a - 314$ , $2200 a + 3186\bigr]$	${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-194a-314\right){x}+2200a+3186$
784.1-e2	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{8} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$8.330553587$	1.472647733	$-\frac{110288896}{49} a + \frac{155981824}{49}$	$\bigl[0$ , $a + 1$ , $0$ , $6 a + 7$ , $23 a + 32\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+7\right){x}+23a+32$
784.1-e3	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{8} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$4.165276793$	1.472647733	$\frac{13282665232}{5764801} a + \frac{23566456972}{5764801}$	$\bigl[a$ , $-a - 1$ , $0$ , $-15 a + 18$ , $30 a - 43\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+18\right){x}+30a-43$
784.1-e4	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{4} \cdot 7^{6}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2}$	$1$	$16.66110717$	1.472647733	$\frac{4566144}{2401} a + \frac{14497232}{2401}$	$\bigl[a$ , $-a - 1$ , $0$ , $5 a - 7$ , $7 a - 9\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-7\right){x}+7a-9$
784.1-e5	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$2^{8} \cdot 7^{6}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$16.66110717$	1.472647733	$\frac{53744933616}{2401} a + \frac{76065896132}{2401}$	$\bigl[a$ , $-a - 1$ , $0$ , $25 a - 52$ , $-84 a + 159\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-52\right){x}-84a+159$
784.1-e6	784.1-e	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{10} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$8.330553587$	1.472647733	$\frac{69495892205440052}{49} a + \frac{98282033286152638}{49}$	$\bigl[a$ , $-a - 1$ , $0$ , $-115 a - 122$ , $322 a + 1587\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-115a-122\right){x}+322a+1587$
784.1-f1	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$7.680735453$	1.357775030	$-\frac{551719468601289472}{49} a + \frac{780249146376863552}{49}$	$\bigl[0$ , $-a$ , $0$ , $1562 a - 3681$ , $-52607 a + 96844\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(1562a-3681\right){x}-52607a+96844$
784.1-f2	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	$2$	$1$	$7.680735453$	1.357775030	$-\frac{13219923200}{117649} a + \frac{18683377472}{117649}$	$\bigl[0$ , $-a$ , $0$ , $22 a - 41$ , $-51 a + 132\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(22a-41\right){x}-51a+132$
784.1-f3	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$7.680735453$	1.357775030	$-\frac{210688}{49} a + \frac{302912}{49}$	$\bigl[0$ , $-a$ , $0$ , $2 a - 1$ , $a - 4\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(2a-1\right){x}+a-4$
784.1-f4	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$7.680735453$	1.357775030	$\frac{210688}{49} a + \frac{302912}{49}$	$\bigl[0$ , $a$ , $0$ , $-2 a - 1$ , $-a - 4\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-2a-1\right){x}-a-4$
784.1-f5	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{9}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	$2$	$1$	$7.680735453$	1.357775030	$\frac{13219923200}{117649} a + \frac{18683377472}{117649}$	$\bigl[0$ , $a$ , $0$ , $-22 a - 41$ , $51 a + 132\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-22a-41\right){x}+51a+132$
784.1-f6	784.1-f	$6$	$18$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	784.1	$2^{4} \cdot 7^{2}$	$- 2^{12} \cdot 7^{3}$	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$7.680735453$	1.357775030	$\frac{551719468601289472}{49} a + \frac{780249146376863552}{49}$	$\bigl[0$ , $a$ , $0$ , $-1562 a - 3681$ , $52607 a + 96844\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-1562a-3681\right){x}+52607a+96844$

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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.