Elliptic curves over Q(2)\Q(\sqrt{2}) of conductor 3600.1

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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
3600.1-a1	3600.1-a	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$5.750549845$	2.033126395	$-\frac{77824}{75} a - \frac{8192}{25}$	$\bigl[0$ , $a - 1$ , $0$ , $-4 a - 3$ , $-5 a - 8\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-3\right){x}-5a-8$
3600.1-a2	3600.1-a	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$11.50109969$	2.033126395	$\frac{32153888}{15} a + \frac{136532464}{45}$	$\bigl[a$ , $a - 1$ , $a$ , $10 a - 16$ , $-20 a + 27\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-16\right){x}-20a+27$
3600.1-b1	3600.1-b	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.184365542$	$24.51599364$	3.196055094	$-\frac{4554752}{15} a + \frac{19595264}{45}$	$\bigl[0$ , $a$ , $0$ , $-12 a - 18$ , $18 a + 27\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-12a-18\right){x}+18a+27$
3600.1-b2	3600.1-b	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$0.368731084$	$24.51599364$	3.196055094	$\frac{242852032}{25} a + \frac{1030477264}{75}$	$\bigl[a$ , $-1$ , $0$ , $5 a - 11$ , $-3 a + 8\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(5a-11\right){x}-3a+8$
3600.1-c1	3600.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$- 2^{8} \cdot 3^{2} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	$2^{2}$	$1$	$1.577788215$	2.231329492	$-\frac{67647399956}{1875} a + \frac{95664054076}{1875}$	$\bigl[a$ , $-a + 1$ , $0$ , $-10 a - 50$ , $-50 a - 200\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-50\right){x}-50a-200$
3600.1-c2	3600.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{8} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$12.62230572$	2.231329492	$-\frac{118784}{135} a + \frac{1933312}{405}$	$\bigl[0$ , $a$ , $0$ , $-6 a - 10$ , $-12 a - 15\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-6a-10\right){x}-12a-15$
3600.1-c3	3600.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{4} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$4$	$2^{2}$	$1$	$6.311152861$	2.231329492	$\frac{583258208}{225} a + \frac{275765456}{75}$	$\bigl[a$ , $-a + 1$ , $0$ , $-25 a - 35$ , $-80 a - 116\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a-35\right){x}-80a-116$
3600.1-c4	3600.1-c	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$- 2^{8} \cdot 3^{2} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$16$	$1$	$1$	$1.577788215$	2.231329492	$\frac{285884843213476}{15} a + \frac{404302222551364}{15}$	$\bigl[a$ , $-1$ , $a$ , $-46 a + 31$ , $436 a - 685\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-46a+31\right){x}+436a-685$
3600.1-d1	3600.1-d	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{8} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$4.463033054$	1.577920468	$-\frac{865504}{675} a - \frac{3363568}{2025}$	$\bigl[a$ , $a - 1$ , $a$ , $-3 a$ , $-4 a + 1\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-3a{x}-4a+1$
3600.1-d2	3600.1-d	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$8.926066109$	1.577920468	$\frac{276826112}{45} a + \frac{130648064}{15}$	$\bigl[0$ , $-a - 1$ , $0$ , $-13$ , $-9 a + 2\bigr]$	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-13{x}-9a+2$
3600.1-e1	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{32} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{6}$	$1$	$1.273994615$	1.801700464	$-\frac{147281603041}{215233605}$	$\bigl[a$ , $0$ , $a$ , $-441$ , $6598\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-441{x}+6598$
3600.1-e2	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{2} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$5.095978463$	1.801700464	$-\frac{1}{15}$	$\bigl[a$ , $0$ , $a$ , $-1$ , $-2\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}-2$
3600.1-e3	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{4} \cdot 5^{16}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{6}$	$1$	$1.273994615$	1.801700464	$\frac{4733169839}{3515625}$	$\bigl[a$ , $0$ , $a$ , $139$ , $362\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+139{x}+362$
3600.1-e4	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{8} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$1$	$5.095978463$	1.801700464	$\frac{111284641}{50625}$	$\bigl[a$ , $0$ , $a$ , $-41$ , $38\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-41{x}+38$
3600.1-e5	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{4} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$5.095978463$	1.801700464	$\frac{13997521}{225}$	$\bigl[a$ , $0$ , $a$ , $-21$ , $-38\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-21{x}-38$
3600.1-e6	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{16} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$1$	$5.095978463$	1.801700464	$\frac{272223782641}{164025}$	$\bigl[a$ , $0$ , $a$ , $-541$ , $4738\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-541{x}+4738$
3600.1-e7	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{2} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	$2^{2}$	$1$	$1.273994615$	1.801700464	$\frac{56667352321}{15}$	$\bigl[a$ , $0$ , $a$ , $-321$ , $-2258\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-321{x}-2258$
3600.1-e8	3600.1-e	$8$	$16$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{8} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	$2^{4}$	$1$	$5.095978463$	1.801700464	$\frac{1114544804970241}{405}$	$\bigl[a$ , $0$ , $a$ , $-8641$ , $307678\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-8641{x}+307678$
3600.1-f1	3600.1-f	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{12} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$2.366392344$	0.836646036	$\frac{24897088}{18225}$	$\bigl[0$ , $-a + 1$ , $0$ , $48 a + 74$ , $-126 a - 176\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(48a+74\right){x}-126a-176$
3600.1-f2	3600.1-f	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{12} \cdot 3^{6} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2$	$1$	$4.732784688$	0.836646036	$\frac{36594368}{16875}$	$\bigl[0$ , $a - 1$ , $0$ , $-56 a - 82$ , $-134 a - 188\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-56a-82\right){x}-134a-188$
3600.1-g1	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{36} \cdot 3^{2} \cdot 5^{6}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{2} \cdot 3$	$1$	$2.683744567$	2.846540973	$-\frac{273359449}{1536000}$	$\bigl[a$ , $-1$ , $0$ , $-54$ , $510\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-54{x}+510$
3600.1-g2	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{20} \cdot 3^{6} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{2} \cdot 3$	$1$	$2.683744567$	2.846540973	$\frac{357911}{2160}$	$\bigl[a$ , $-1$ , $0$ , $6$ , $-18\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+6{x}-18$
3600.1-g3	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{18} \cdot 3^{2} \cdot 5^{24}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{4} \cdot 3$	$1$	$0.670936141$	2.846540973	$\frac{10316097499609}{5859375000}$	$\bigl[a$ , $-1$ , $0$ , $-1814$ , $4350\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1814{x}+4350$
3600.1-g4	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{14} \cdot 3^{24} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{4} \cdot 3$	$1$	$2.683744567$	2.846540973	$\frac{35578826569}{5314410}$	$\bigl[a$ , $-1$ , $0$ , $-274$ , $1550\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-274{x}+1550$
3600.1-g5	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{16} \cdot 3^{12} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2^{4} \cdot 3$	$1$	$2.683744567$	2.846540973	$\frac{702595369}{72900}$	$\bigl[a$ , $-1$ , $0$ , $-74$ , $-210\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-74{x}-210$
3600.1-g6	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{24} \cdot 3^{4} \cdot 5^{12}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2^{4} \cdot 3$	$1$	$2.683744567$	2.846540973	$\frac{4102915888729}{9000000}$	$\bigl[a$ , $-1$ , $0$ , $-1334$ , $18942\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1334{x}+18942$
3600.1-g7	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{14} \cdot 3^{6} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{4} \cdot 3$	$1$	$0.670936141$	2.846540973	$\frac{2656166199049}{33750}$	$\bigl[a$ , $-1$ , $0$ , $-1154$ , $-14898\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1154{x}-14898$
3600.1-g8	3600.1-g	$8$	$12$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{18} \cdot 3^{8} \cdot 5^{6}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{4} \cdot 3$	$1$	$2.683744567$	2.846540973	$\frac{16778985534208729}{81000}$	$\bigl[a$ , $-1$ , $0$ , $-21334$ , $1202942\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-21334{x}+1202942$
3600.1-h1	3600.1-h	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$12.56719702$	2.221587558	$-\frac{161792}{15} a + \frac{772096}{45}$	$\bigl[0$ , $a$ , $0$ , $-2 a - 4$ , $-2 a - 3\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-2a-4\right){x}-2a-3$
3600.1-h2	3600.1-h	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$12.56719702$	2.221587558	$\frac{22335584}{75} a + \frac{10601168}{25}$	$\bigl[a$ , $-a + 1$ , $a$ , $-9 a - 12$ , $-16 a - 23\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-12\right){x}-16a-23$
3600.1-i1	3600.1-i	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$5.750549845$	2.033126395	$\frac{77824}{75} a - \frac{8192}{25}$	$\bigl[0$ , $-a - 1$ , $0$ , $4 a - 3$ , $5 a - 8\bigr]$	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-3\right){x}+5a-8$
3600.1-i2	3600.1-i	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$11.50109969$	2.033126395	$-\frac{32153888}{15} a + \frac{136532464}{45}$	$\bigl[a$ , $-a - 1$ , $a$ , $-10 a - 16$ , $20 a + 27\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-16\right){x}+20a+27$
3600.1-j1	3600.1-j	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$12.56719702$	2.221587558	$-\frac{22335584}{75} a + \frac{10601168}{25}$	$\bigl[a$ , $a + 1$ , $a$ , $9 a - 12$ , $16 a - 23\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-12\right){x}+16a-23$
3600.1-j2	3600.1-j	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$12.56719702$	2.221587558	$\frac{161792}{15} a + \frac{772096}{45}$	$\bigl[0$ , $-a$ , $0$ , $2 a - 4$ , $2 a - 3\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(2a-4\right){x}+2a-3$
3600.1-k1	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{10} \cdot 3^{2} \cdot 5^{16}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{5}$	$0.760464508$	$2.911019061$	3.130682295	$-\frac{27995042}{1171875}$	$\bigl[a$ , $-1$ , $0$ , $-20$ , $300\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-20{x}+300$
3600.1-k2	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{16} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{4}$	$0.380232254$	$2.911019061$	3.130682295	$\frac{54607676}{32805}$	$\bigl[a$ , $-1$ , $0$ , $20$ , $-10\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+20{x}-10$
3600.1-k3	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{8} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.760464508$	$11.64407624$	3.130682295	$\frac{3631696}{2025}$	$\bigl[a$ , $-1$ , $0$ , $-5$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-5{x}$
3600.1-k4	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1.520929017$	$11.64407624$	3.130682295	$\frac{868327204}{5625}$	$\bigl[a$ , $-1$ , $0$ , $-50$ , $144\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-50{x}+144$
3600.1-k5	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1.520929017$	$5.822038123$	3.130682295	$\frac{24918016}{45}$	$\bigl[0$ , $-1$ , $0$ , $-15$ , $-18\bigr]$	${y}^2={x}^{3}-{x}^{2}-15{x}-18$
3600.1-k6	3600.1-k	$6$	$8$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{10} \cdot 3^{2} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$0.760464508$	$11.64407624$	3.130682295	$\frac{1770025017602}{75}$	$\bigl[a$ , $-1$ , $0$ , $-800$ , $8844\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-800{x}+8844$
3600.1-l1	3600.1-l	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{8} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$4.463033054$	1.577920468	$\frac{865504}{675} a - \frac{3363568}{2025}$	$\bigl[a$ , $-a - 1$ , $a$ , $3 a$ , $4 a + 1\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+3a{x}+4a+1$
3600.1-l2	3600.1-l	$2$	$2$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$8.926066109$	1.577920468	$-\frac{276826112}{45} a + \frac{130648064}{15}$	$\bigl[0$ , $a - 1$ , $0$ , $-13$ , $9 a + 2\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}-13{x}+9a+2$
3600.1-m1	3600.1-m	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$1$	$0.891621139$	$15.64258266$	2.465550068	$\frac{21296}{15}$	$\bigl[a$ , $-1$ , $0$ , $1$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+{x}$
3600.1-m2	3600.1-m	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{4} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.445810569$	$15.64258266$	2.465550068	$\frac{470596}{225}$	$\bigl[a$ , $-1$ , $0$ , $-4$ , $2\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4{x}+2$
3600.1-m3	3600.1-m	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{10} \cdot 3^{2} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{4}$	$0.222905284$	$3.910645665$	2.465550068	$\frac{136835858}{1875}$	$\bigl[a$ , $-1$ , $0$ , $-34$ , $-70\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-34{x}-70$
3600.1-m4	3600.1-m	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{10} \cdot 3^{8} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{4}$	$0.222905284$	$15.64258266$	2.465550068	$\frac{546718898}{405}$	$\bigl[a$ , $-1$ , $0$ , $-54$ , $162\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-54{x}+162$
3600.1-n1	3600.1-n	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$- 2^{8} \cdot 3^{2} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$16$	$1$	$1$	$1.577788215$	2.231329492	$-\frac{285884843213476}{15} a + \frac{404302222551364}{15}$	$\bigl[a$ , $-1$ , $a$ , $46 a + 31$ , $-436 a - 685\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(46a+31\right){x}-436a-685$
3600.1-n2	3600.1-n	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{8} \cdot 3^{8} \cdot 5^{2}$	$1.95776$	$(a), (3), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$12.62230572$	2.231329492	$\frac{118784}{135} a + \frac{1933312}{405}$	$\bigl[0$ , $-a$ , $0$ , $6 a - 10$ , $12 a - 15\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(6a-10\right){x}+12a-15$
3600.1-n3	3600.1-n	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3^{4} \cdot 5^{4}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$4$	$2^{2}$	$1$	$6.311152861$	2.231329492	$-\frac{583258208}{225} a + \frac{275765456}{75}$	$\bigl[a$ , $a + 1$ , $0$ , $25 a - 35$ , $80 a - 116\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-35\right){x}+80a-116$
3600.1-n4	3600.1-n	$4$	$4$	$\Q(\sqrt{2})$	$2$	$[2, 0]$	3600.1	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$- 2^{8} \cdot 3^{2} \cdot 5^{8}$	$1.95776$	$(a), (3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	$2^{2}$	$1$	$1.577788215$	2.231329492	$\frac{67647399956}{1875} a + \frac{95664054076}{1875}$	$\bigl[a$ , $a + 1$ , $0$ , $10 a - 50$ , $50 a - 200\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-50\right){x}+50a-200$

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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.