Elliptic curves over Q(7)\Q(\sqrt{7}) of conductor 567.1

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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
567.1-a1	567.1-a	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{23} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$2.566767726$	$1.735260738$	6.733832077	$-\frac{422830592}{45927} a + \frac{1117795136}{45927}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $40 a - 95$ , $189 a - 520\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-95\right){x}+189a-520$
567.1-a2	567.1-a	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{19} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$5.133535453$	$1.735260738$	6.733832077	$\frac{108334592}{3969} a + \frac{286626496}{3969}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-122 a + 337$ , $311067 a - 822994\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-122a+337\right){x}+311067a-822994$
567.1-b1	567.1-b	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{15} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	$2^{3}$	$1$	$2.751645710$	1.040024320	$-\frac{224768}{7} a + \frac{580672}{7}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-53 a - 143$ , $-629 a - 1666\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-53a-143\right){x}-629a-1666$
567.1-b2	567.1-b	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{9} \cdot 7^{6}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$8.254937131$	1.040024320	$-\frac{1204736}{343} a + \frac{3558976}{343}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $148 a - 380$ , $-1528 a + 4054\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(148a-380\right){x}-1528a+4054$
567.1-b3	567.1-b	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{9} \cdot 7^{3}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3$	$1$	$16.50987426$	1.040024320	$-\frac{3312820736}{49} a + \frac{1252147264}{7}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-8 a - 32$ , $-7 a + 1\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-32\right){x}-7a+1$
567.1-b4	567.1-b	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{15} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$5.503291420$	1.040024320	$\frac{9461248}{7} a + 3577792$	$\bigl[a + 1$ , $a + 1$ , $1$ , $19 a - 41$ , $-17 a + 41\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-41\right){x}-17a+41$
567.1-c1	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{14} \cdot 7^{16}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{8}$	$2.638508823$	$0.271340145$	4.329558047	$-\frac{4354703137}{17294403}$	$\bigl[a$ , $-1$ , $0$ , $-306$ , $-5859\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-306{x}-5859$
567.1-c2	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{32} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.638508823$	$2.170721162$	4.329558047	$-\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721}$	$\bigl[a$ , $-1$ , $0$ , $1035 a - 2871$ , $-29241 a + 82944\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}-29241a+82944$
567.1-c3	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1.319254411$	$4.341442324$	4.329558047	$\frac{103823}{63}$	$\bigl[a$ , $-1$ , $0$ , $9$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+9{x}$
567.1-c4	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{20} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{6}$	$0.659627205$	$4.341442324$	4.329558047	$\frac{7189057}{3969}$	$\bigl[a$ , $-1$ , $0$ , $-36$ , $-27\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-36{x}-27$
567.1-c5	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{28} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$1.319254411$	$4.341442324$	4.329558047	$\frac{6570725617}{45927}$	$\bigl[a$ , $-1$ , $0$ , $-351$ , $2430\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-351{x}+2430$
567.1-c6	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{8}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{7}$	$1.319254411$	$1.085360581$	4.329558047	$\frac{13027640977}{21609}$	$\bigl[a$ , $-1$ , $0$ , $-441$ , $-3672\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-441{x}-3672$
567.1-c7	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{32} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.638508823$	$2.170721162$	4.329558047	$\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721}$	$\bigl[a$ , $-1$ , $0$ , $-1035 a - 2871$ , $29241 a + 82944\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-1035a-2871\right){x}+29241a+82944$
567.1-c8	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{14} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	$2^{4}$	$2.638508823$	$0.271340145$	4.329558047	$\frac{53297461115137}{147}$	$\bigl[a$ , $-1$ , $0$ , $-7056$ , $-229905\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-7056{x}-229905$
567.1-d1	567.1-d	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{15} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$5.503291420$	1.040024320	$-\frac{9461248}{7} a + 3577792$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-14 a - 44$ , $-27 a - 76\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-44\right){x}-27a-76$
567.1-d2	567.1-d	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{9} \cdot 7^{6}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$8.254937131$	1.040024320	$\frac{1204736}{343} a + \frac{3558976}{343}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-143 a - 377$ , $1148 a + 3037\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a-377\right){x}+1148a+3037$
567.1-d3	567.1-d	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{15} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	$2^{3}$	$1$	$2.751645710$	1.040024320	$\frac{224768}{7} a + \frac{580672}{7}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $58 a - 140$ , $486 a - 1276\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(58a-140\right){x}+486a-1276$
567.1-d4	567.1-d	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{9} \cdot 7^{3}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3$	$1$	$16.50987426$	1.040024320	$\frac{3312820736}{49} a + \frac{1252147264}{7}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $13 a - 35$ , $-28 a + 73\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-35\right){x}-28a+73$
567.1-e1	567.1-e	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{17} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$0.190615875$	$7.512474961$	2.164975951	$-\frac{17359374619}{63} a + \frac{45928588514}{63}$	$\bigl[a$ , $-1$ , $1$ , $349 a + 924$ , $100940 a + 267062\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(349a+924\right){x}+100940a+267062$
567.1-e2	567.1-e	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{16} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.381231750$	$15.02494992$	2.164975951	$\frac{266548}{21} a - \frac{11591}{3}$	$\bigl[1$ , $-1$ , $a$ , $664 a - 1758$ , $-15679 a + 41481\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(664a-1758\right){x}-15679a+41481$
567.1-f1	567.1-f	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{19} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$5.625830929$	4.252728444	$-\frac{108334592}{3969} a + \frac{286626496}{3969}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $127 a + 334$ , $311316 a + 823663\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a+334\right){x}+311316a+823663$
567.1-f2	567.1-f	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{23} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$5.625830929$	4.252728444	$\frac{422830592}{45927} a + \frac{1117795136}{45927}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-35 a - 98$ , $114 a + 325\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-98\right){x}+114a+325$
567.1-g1	567.1-g	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{16} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$2.736190556$	1.034182821	$-\frac{266548}{21} a - \frac{11591}{3}$	$\bigl[a$ , $-1$ , $1$ , $-665 a - 1758$ , $-15679 a - 41483\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-665a-1758\right){x}-15679a-41483$
567.1-g2	567.1-g	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{17} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$1.368095278$	1.034182821	$\frac{17359374619}{63} a + \frac{45928588514}{63}$	$\bigl[1$ , $-1$ , $a$ , $-350 a + 924$ , $100940 a - 267064\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-350a+924\right){x}+100940a-267064$
567.1-h1	567.1-h	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{19} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$5.133535453$	$1.735260738$	6.733832077	$-\frac{108334592}{3969} a + \frac{286626496}{3969}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $127 a + 334$ , $-310733 a - 822124\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a+334\right){x}-310733a-822124$
567.1-h2	567.1-h	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{23} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$2.566767726$	$1.735260738$	6.733832077	$\frac{422830592}{45927} a + \frac{1117795136}{45927}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-35 a - 98$ , $-287 a - 784\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-98\right){x}-287a-784$
567.1-i1	567.1-i	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{16} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.381231750$	$15.02494992$	2.164975951	$-\frac{266548}{21} a - \frac{11591}{3}$	$\bigl[1$ , $-1$ , $a$ , $-665 a - 1758$ , $15679 a + 41481\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-665a-1758\right){x}+15679a+41481$
567.1-i2	567.1-i	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{17} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$0.190615875$	$7.512474961$	2.164975951	$\frac{17359374619}{63} a + \frac{45928588514}{63}$	$\bigl[a$ , $-1$ , $1$ , $-350 a + 924$ , $-100940 a + 267062\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-350a+924\right){x}-100940a+267062$
567.1-j1	567.1-j	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{15} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{2}$	$0.585879788$	$13.23033863$	2.929749280	$-\frac{9461248}{7} a + 3577792$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-14 a - 44$ , $-50 a - 128\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-44\right){x}-50a-128$
567.1-j2	567.1-j	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{9} \cdot 7^{6}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{3}$	$0.878819682$	$4.410112877$	2.929749280	$\frac{1204736}{343} a + \frac{3558976}{343}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-143 a - 377$ , $-1819 a - 4813\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a-377\right){x}-1819a-4813$
567.1-j3	567.1-j	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{15} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{3}$	$0.292939894$	$13.23033863$	2.929749280	$\frac{224768}{7} a + \frac{580672}{7}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $58 a - 140$ , $-518 a + 1381\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(58a-140\right){x}-518a+1381$
567.1-j4	567.1-j	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{9} \cdot 7^{3}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{2}$	$1.757639365$	$4.410112877$	2.929749280	$\frac{3312820736}{49} a + \frac{1252147264}{7}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $13 a - 35$ , $14 a - 70\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-35\right){x}+14a-70$
567.1-k1	567.1-k	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{17} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$1.368095278$	1.034182821	$-\frac{17359374619}{63} a + \frac{45928588514}{63}$	$\bigl[1$ , $-1$ , $a$ , $349 a + 924$ , $-100940 a - 267064\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(349a+924\right){x}-100940a-267064$
567.1-k2	567.1-k	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{16} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$2.736190556$	1.034182821	$\frac{266548}{21} a - \frac{11591}{3}$	$\bigl[a$ , $-1$ , $1$ , $664 a - 1758$ , $15679 a - 41483\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(664a-1758\right){x}+15679a-41483$
567.1-l1	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{14} \cdot 7^{16}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	$2^{3}$	$1$	$1.217293980$	1.840375511	$-\frac{4354703137}{17294403}$	$\bigl[1$ , $-1$ , $0$ , $-306$ , $5859\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$
567.1-l2	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{32} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$16$	$2^{3}$	$1$	$0.304323495$	1.840375511	$-\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721}$	$\bigl[1$ , $-1$ , $0$ , $1035 a - 2871$ , $29241 a - 82944\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}+29241a-82944$
567.1-l3	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$4.869175922$	1.840375511	$\frac{103823}{63}$	$\bigl[1$ , $-1$ , $0$ , $9$ , $0\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$
567.1-l4	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{20} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$1$	$4.869175922$	1.840375511	$\frac{7189057}{3969}$	$\bigl[1$ , $-1$ , $0$ , $-36$ , $27\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$
567.1-l5	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{28} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	$2^{5}$	$1$	$1.217293980$	1.840375511	$\frac{6570725617}{45927}$	$\bigl[1$ , $-1$ , $0$ , $-351$ , $-2430\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$
567.1-l6	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{8}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$1$	$4.869175922$	1.840375511	$\frac{13027640977}{21609}$	$\bigl[1$ , $-1$ , $0$ , $-441$ , $3672\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-441{x}+3672$
567.1-l7	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{32} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$16$	$2^{3}$	$1$	$0.304323495$	1.840375511	$\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721}$	$\bigl[1$ , $-1$ , $0$ , $-1035 a - 2871$ , $-29241 a - 82944\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1035a-2871\right){x}-29241a-82944$
567.1-l8	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{14} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{5}$	$1$	$4.869175922$	1.840375511	$\frac{53297461115137}{147}$	$\bigl[1$ , $-1$ , $0$ , $-7056$ , $229905\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$
567.1-m1	567.1-m	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{15} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{3}$	$0.292939894$	$13.23033863$	2.929749280	$-\frac{224768}{7} a + \frac{580672}{7}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $-53 a - 143$ , $375 a + 991\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-53a-143\right){x}+375a+991$
567.1-m2	567.1-m	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{9} \cdot 7^{6}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{3}$	$0.878819682$	$4.410112877$	2.929749280	$-\frac{1204736}{343} a + \frac{3558976}{343}$	$\bigl[a + 1$ , $a + 1$ , $a$ , $148 a - 380$ , $1439 a - 3796\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(148a-380\right){x}+1439a-3796$
567.1-m3	567.1-m	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{9} \cdot 7^{3}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{2}$	$1.757639365$	$4.410112877$	2.929749280	$-\frac{3312820736}{49} a + \frac{1252147264}{7}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-8 a - 32$ , $-49 a - 142\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-32\right){x}-49a-142$
567.1-m4	567.1-m	$4$	$6$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{15} \cdot 7$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	$2^{2}$	$0.585879788$	$13.23033863$	2.929749280	$\frac{9461248}{7} a + 3577792$	$\bigl[a + 1$ , $a + 1$ , $1$ , $19 a - 41$ , $6 a - 11\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-41\right){x}+6a-11$
567.1-n1	567.1-n	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{23} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$5.625830929$	4.252728444	$-\frac{422830592}{45927} a + \frac{1117795136}{45927}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $40 a - 95$ , $-212 a + 589\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-95\right){x}-212a+589$
567.1-n2	567.1-n	$2$	$2$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$- 3^{19} \cdot 7^{4}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$1$	$5.625830929$	4.252728444	$\frac{108334592}{3969} a + \frac{286626496}{3969}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $-122 a + 337$ , $-310982 a + 822793\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-122a+337\right){x}-310982a+822793$

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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.