Elliptic curves over Q(5)\Q(\sqrt{5}) of conductor 1280.1

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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
1280.1-a1	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	$2$	$1$	$1.498444490$	1.340249496	$-\frac{1565563717889316}{5} a + \frac{2533135307076378}{5}$	$\bigl[0$ , $0$ , $0$ , $173 \phi - 547$ , $3764 \phi - 4110\bigr]$	${y}^2={x}^{3}+\left(173\phi-547\right){x}+3764\phi-4110$
1280.1-a2	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$1$	$1$	$11.98755592$	1.340249496	$-\frac{237035808}{5} a + \frac{383532624}{5}$	$\bigl[0$ , $0$ , $0$ , $8 \phi - 7$ , $-16 \phi + 6\bigr]$	${y}^2={x}^{3}+\left(8\phi-7\right){x}-16\phi+6$
1280.1-a3	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$2.996888981$	1.340249496	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $13 \phi + 13$ , $68 \phi + 34\bigr]$	${y}^2={x}^{3}+\left(13\phi+13\right){x}+68\phi+34$
1280.1-a4	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{2}$	$1$	$11.98755592$	1.340249496	$\frac{148176}{25}$	$\bigl[0$ , $0$ , $0$ , $-7 \phi - 7$ , $12 \phi + 6\bigr]$	${y}^2={x}^{3}+\left(-7\phi-7\right){x}+12\phi+6$
1280.1-a5	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2$	$1$	$23.97511185$	1.340249496	$\frac{55296}{5}$	$\bigl[0$ , $0$ , $0$ , $2 \phi - 4$ , $-2 \phi + 3\bigr]$	${y}^2={x}^{3}+\left(2\phi-4\right){x}-2\phi+3$
1280.1-a6	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{3}$	$1$	$5.993777963$	1.340249496	$\frac{132304644}{5}$	$\bigl[0$ , $0$ , $0$ , $-107 \phi - 107$ , $852 \phi + 426\bigr]$	${y}^2={x}^{3}+\left(-107\phi-107\right){x}+852\phi+426$
1280.1-a7	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2$	$1$	$5.993777963$	1.340249496	$\frac{237035808}{5} a + \frac{146496816}{5}$	$\bigl[0$ , $0$ , $0$ , $-8 \phi + 1$ , $-16 \phi + 10\bigr]$	${y}^2={x}^{3}+\left(-8\phi+1\right){x}-16\phi+10$
1280.1-a8	1280.1-a	$8$	$16$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$2.996888981$	1.340249496	$\frac{1565563717889316}{5} a + \frac{967571589187062}{5}$	$\bigl[0$ , $0$ , $0$ , $-173 \phi - 374$ , $3764 \phi + 346\bigr]$	${y}^2={x}^{3}+\left(-173\phi-374\right){x}+3764\phi+346$
1280.1-b1	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$1$	$6.484547005$	1.449988790	$-\frac{1613607658}{625} a + \frac{522073008}{125}$	$\bigl[0$ , $-\phi + 1$ , $0$ , $60 \phi - 144$ , $-276 \phi + 676\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(60\phi-144\right){x}-276\phi+676$
1280.1-b2	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$1$	$1$	$12.96909401$	1.449988790	$\frac{2816}{5} a + \frac{1792}{5}$	$\bigl[0$ , $-\phi + 1$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+{x}$
1280.1-b3	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2}$	$1$	$12.96909401$	1.449988790	$-\frac{53328}{5} a + \frac{97888}{5}$	$\bigl[0$ , $-\phi + 1$ , $0$ , $-4$ , $4 \phi - 4\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}-4{x}+4\phi-4$
1280.1-b4	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$3.242273502$	1.449988790	$-\frac{1444495316}{5} a + \frac{2337509148}{5}$	$\bigl[0$ , $-\phi + 1$ , $0$ , $20 \phi - 64$ , $108 \phi - 236\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(20\phi-64\right){x}+108\phi-236$
1280.1-b5	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$12.96909401$	1.449988790	$\frac{22755876}{25} a + \frac{14144708}{25}$	$\bigl[0$ , $-\phi + 1$ , $0$ , $-20 \phi - 24$ , $76 \phi + 52\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-20\phi-24\right){x}+76\phi+52$
1280.1-b6	1280.1-b	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$6.484547005$	1.449988790	$\frac{9285883494578}{5} a + \frac{5738991619552}{5}$	$\bigl[0$ , $\phi$ , $0$ , $-165 \phi + 136$ , $-379 \phi + 1125\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(-165\phi+136\right){x}-379\phi+1125$
1280.1-c1	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$2.804604675$	1.254257341	$-\frac{1613607658}{625} a + \frac{522073008}{125}$	$\bigl[0$ , $1$ , $0$ , $-24 \phi - 84$ , $-524 \phi - 124\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-24\phi-84\right){x}-524\phi-124$
1280.1-c2	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$1$	$1$	$11.21841870$	1.254257341	$\frac{2816}{5} a + \frac{1792}{5}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $\phi + 1$ , $-1\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi+1\right){x}-1$
1280.1-c3	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2}$	$1$	$11.21841870$	1.254257341	$-\frac{53328}{5} a + \frac{97888}{5}$	$\bigl[0$ , $1$ , $0$ , $-4 \phi - 4$ , $-4 \phi - 4\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-4\phi-4\right){x}-4\phi-4$
1280.1-c4	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$1$	$5.609209351$	1.254257341	$-\frac{1444495316}{5} a + \frac{2337509148}{5}$	$\bigl[0$ , $1$ , $0$ , $-24 \phi - 44$ , $148 \phi + 20\bigr]$	${y}^2={x}^{3}+{x}^{2}+\left(-24\phi-44\right){x}+148\phi+20$
1280.1-c5	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{3}$	$1$	$5.609209351$	1.254257341	$\frac{22755876}{25} a + \frac{14144708}{25}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $6 \phi - 29$ , $-33 \phi + 33\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(6\phi-29\right){x}-33\phi+33$
1280.1-c6	1280.1-c	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$1.402302337$	1.254257341	$\frac{9285883494578}{5} a + \frac{5738991619552}{5}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $-194 \phi - 29$ , $-1113 \phi - 367\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-194\phi-29\right){x}-1113\phi-367$
1280.1-d1	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{12}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3} \cdot 3$	$1$	$2.141031885$	1.436247851	$-\frac{20720464}{15625}$	$\bigl[0$ , $\phi - 1$ , $0$ , $36 \phi - 72$ , $-280 \phi + 420\bigr]$	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-72\right){x}-280\phi+420$
1280.1-d2	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$6.423095656$	1.436247851	$\frac{21296}{25}$	$\bigl[0$ , $\phi$ , $0$ , $4 \phi + 4$ , $8 \phi + 4\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(4\phi+4\right){x}+8\phi+4$
1280.1-d3	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{3}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2 \cdot 3$	$1$	$8.564127542$	1.436247851	$-\frac{170403887082176}{25} a + \frac{275719281184688}{25}$	$\bigl[0$ , $\phi$ , $0$ , $59 \phi - 216$ , $-887 \phi + 1049\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(59\phi-216\right){x}-887\phi+1049$
1280.1-d4	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2$	$1$	$25.69238262$	1.436247851	$\frac{16384}{5}$	$\bigl[0$ , $\phi$ , $0$ , $-\phi - 1$ , $0\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(-\phi-1\right){x}$
1280.1-d5	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$6.423095656$	1.436247851	$-\frac{13352896}{5} a + \frac{21733168}{5}$	$\bigl[0$ , $\phi$ , $0$ , $-6 \phi - 11$ , $-19 \phi - 18\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(-6\phi-11\right){x}-19\phi-18$
1280.1-d6	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5^{6}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2Cs, 3B	$1$	$2 \cdot 3$	$1$	$8.564127542$	1.436247851	$\frac{488095744}{125}$	$\bigl[0$ , $\phi - 1$ , $0$ , $41 \phi - 82$ , $-232 \phi + 348\bigr]$	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(41\phi-82\right){x}-232\phi+348$
1280.1-d7	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2$	$1$	$25.69238262$	1.436247851	$\frac{13352896}{5} a + \frac{8380272}{5}$	$\bigl[0$ , $\phi - 1$ , $0$ , $6 \phi - 17$ , $-19 \phi + 37\bigr]$	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(6\phi-17\right){x}-19\phi+37$
1280.1-d8	1280.1-d	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{3}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$2 \cdot 3$	$1$	$2.141031885$	1.436247851	$\frac{170403887082176}{25} a + \frac{105315394102512}{25}$	$\bigl[0$ , $\phi - 1$ , $0$ , $-59 \phi - 157$ , $-887 \phi - 162\bigr]$	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-59\phi-157\right){x}-887\phi-162$
1280.1-e1	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$1$	$0.347404686$	$20.93652055$	1.626391824	$-\frac{2816}{5} a + \frac{4608}{5}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $\phi + 1$ , $0\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi+1\right){x}$
1280.1-e2	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$0.173702343$	$5.234130138$	1.626391824	$-\frac{9285883494578}{5} a + 3004975022826$	$\bigl[0$ , $-\phi - 1$ , $0$ , $196 \phi - 224$ , $-1308 \phi + 1704\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(196\phi-224\right){x}-1308\phi+1704$
1280.1-e3	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{3}$	$0.347404686$	$10.46826027$	1.626391824	$-\frac{22755876}{25} a + \frac{36900584}{25}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $-4 \phi - 24$ , $-28 \phi + 24\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-4\phi-24\right){x}-28\phi+24$
1280.1-e4	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{3}$	$0.173702343$	$20.93652055$	1.626391824	$\frac{53328}{5} a + 8912$	$\bigl[0$ , $-1$ , $0$ , $4 \phi - 8$ , $-4 \phi + 8\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(4\phi-8\right){x}-4\phi+8$
1280.1-e5	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.694809372$	$2.617065069$	1.626391824	$\frac{1613607658}{625} a + \frac{996757382}{625}$	$\bigl[0$ , $-1$ , $0$ , $24 \phi - 108$ , $-524 \phi + 648\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(24\phi-108\right){x}-524\phi+648$
1280.1-e6	1280.1-e	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$0.347404686$	$10.46826027$	1.626391824	$\frac{1444495316}{5} a + \frac{893013832}{5}$	$\bigl[0$ , $-1$ , $0$ , $24 \phi - 68$ , $148 \phi - 168\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(24\phi-68\right){x}+148\phi-168$
1280.1-f1	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{12}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2$	$1$	$5.171827352$	1.156455752	$-\frac{20720464}{15625}$	$\bigl[0$ , $-1$ , $0$ , $-36$ , $140\bigr]$	${y}^2={x}^{3}-{x}^{2}-36{x}+140$
1280.1-f2	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2$	$1$	$5.171827352$	1.156455752	$\frac{21296}{25}$	$\bigl[0$ , $-1$ , $0$ , $4$ , $-4\bigr]$	${y}^2={x}^{3}-{x}^{2}+4{x}-4$
1280.1-f3	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{3}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$1$	$1$	$10.34365470$	1.156455752	$-\frac{170403887082176}{25} a + \frac{275719281184688}{25}$	$\bigl[0$ , $-\phi - 1$ , $0$ , $-98 \phi - 157$ , $563 \phi + 725\bigr]$	${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-98\phi-157\right){x}+563\phi+725$
1280.1-f4	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2$	$1$	$20.68730941$	1.156455752	$\frac{16384}{5}$	$\bigl[0$ , $-1$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^{3}-{x}^{2}-{x}$
1280.1-f5	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$1$	$1$	$10.34365470$	1.156455752	$-\frac{13352896}{5} a + \frac{21733168}{5}$	$\bigl[0$ , $-1$ , $0$ , $5 \phi - 16$ , $17 \phi - 16\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(5\phi-16\right){x}+17\phi-16$
1280.1-f6	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5^{6}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2Cs, 3B	$1$	$2$	$1$	$20.68730941$	1.156455752	$\frac{488095744}{125}$	$\bigl[0$ , $-1$ , $0$ , $-41$ , $116\bigr]$	${y}^2={x}^{3}-{x}^{2}-41{x}+116$
1280.1-f7	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$1$	$1$	$10.34365470$	1.156455752	$\frac{13352896}{5} a + \frac{8380272}{5}$	$\bigl[0$ , $-1$ , $0$ , $-5 \phi - 11$ , $-17 \phi + 1\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-5\phi-11\right){x}-17\phi+1$
1280.1-f8	1280.1-f	$8$	$12$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{3}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	$1$	$1$	$10.34365470$	1.156455752	$\frac{170403887082176}{25} a + \frac{105315394102512}{25}$	$\bigl[0$ , $\phi + 1$ , $0$ , $100 \phi - 256$ , $-464 \phi + 1032\bigr]$	${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(100\phi-256\right){x}-464\phi+1032$
1280.1-g1	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$1$	$1$	$12.96909401$	1.449988790	$-\frac{2816}{5} a + \frac{4608}{5}$	$\bigl[0$ , $\phi$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+{x}$
1280.1-g2	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$6.484547005$	1.449988790	$-\frac{9285883494578}{5} a + 3004975022826$	$\bigl[0$ , $-\phi + 1$ , $0$ , $165 \phi - 29$ , $379 \phi + 746\bigr]$	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(165\phi-29\right){x}+379\phi+746$
1280.1-g3	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5^{4}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4}$	$1$	$12.96909401$	1.449988790	$-\frac{22755876}{25} a + \frac{36900584}{25}$	$\bigl[0$ , $\phi$ , $0$ , $20 \phi - 44$ , $-76 \phi + 128\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(20\phi-44\right){x}-76\phi+128$
1280.1-g4	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{16} \cdot 5^{2}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2}$	$1$	$12.96909401$	1.449988790	$\frac{53328}{5} a + 8912$	$\bigl[0$ , $\phi$ , $0$ , $-4$ , $-4 \phi\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}-4{x}-4\phi$
1280.1-g5	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{5}$	$1$	$6.484547005$	1.449988790	$\frac{1613607658}{625} a + \frac{996757382}{625}$	$\bigl[0$ , $\phi$ , $0$ , $-60 \phi - 84$ , $276 \phi + 400\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(-60\phi-84\right){x}+276\phi+400$
1280.1-g6	1280.1-g	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{20} \cdot 5$	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$3.242273502$	1.449988790	$\frac{1444495316}{5} a + \frac{893013832}{5}$	$\bigl[0$ , $\phi$ , $0$ , $-20 \phi - 44$ , $-108 \phi - 128\bigr]$	${y}^2={x}^{3}+\phi{x}^{2}+\left(-20\phi-44\right){x}-108\phi-128$
1280.1-h1	1280.1-h	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$- 2^{22} \cdot 5^{8}$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.694809372$	$2.617065069$	1.626391824	$-\frac{1613607658}{625} a + \frac{522073008}{125}$	$\bigl[0$ , $-1$ , $0$ , $-24 \phi - 84$ , $524 \phi + 124\bigr]$	${y}^2={x}^{3}-{x}^{2}+\left(-24\phi-84\right){x}+524\phi+124$
1280.1-h2	1280.1-h	$6$	$8$	$\Q(\sqrt{5})$	$2$	$[2, 0]$	1280.1	$2^{8} \cdot 5$	$2^{8} \cdot 5$	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$1$	$0.347404686$	$20.93652055$	1.626391824	$\frac{2816}{5} a + \frac{1792}{5}$	$\bigl[0$ , $\phi + 1$ , $0$ , $\phi + 1$ , $1\bigr]$	${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi+1\right){x}+1$

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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.