Elliptic curves over Q(6)\Q(\sqrt{6}) of conductor 375.2

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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
375.2-a1	375.2-a	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{11}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1.040625144$	$10.53250423$	4.474559968	$-\frac{208058}{75} a + \frac{33551}{25}$	$\bigl[a + 1$ , $a$ , $1$ , $a - 4$ , $a - 1\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-4\right){x}+a-1$
375.2-a2	375.2-a	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{2} \cdot 5^{13}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4}$	$0.520312572$	$5.266252119$	4.474559968	$\frac{14550280309}{1875} a + \frac{35641186181}{1875}$	$\bigl[a + 1$ , $a$ , $1$ , $-34 a - 69$ , $112 a + 223\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34a-69\right){x}+112a+223$
375.2-b1	375.2-b	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{11}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$5.373592794$	1.096880035	$-\frac{208058}{75} a + \frac{33551}{25}$	$\bigl[1$ , $-a$ , $0$ , $168 a - 410$ , $-1498 a + 3669\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(168a-410\right){x}-1498a+3669$
375.2-b2	375.2-b	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{2} \cdot 5^{13}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3}$	$1$	$2.686796397$	1.096880035	$\frac{14550280309}{1875} a + \frac{35641186181}{1875}$	$\bigl[1$ , $-a$ , $0$ , $-247 a + 605$ , $-8721 a + 21362\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-247a+605\right){x}-8721a+21362$
375.2-c1	375.2-c	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{5}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$1$	$2^{2}$	$1$	$20.38989080$	4.162069031	$-\frac{81720253739776}{75} a + \frac{66724211524672}{25}$	$\bigl[a$ , $a + 1$ , $a + 1$ , $1241 a - 3040$ , $-37209 a + 91141\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1241a-3040\right){x}-37209a+91141$
375.2-c2	375.2-c	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{5} \cdot 5^{13}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	$2^{2} \cdot 5$	$1$	$4.077978161$	4.162069031	$-\frac{8297016064}{263671875} a + \frac{155957523008}{87890625}$	$\bigl[a$ , $a + 1$ , $a + 1$ , $356 a + 870$ , $-179 a - 439\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(356a+870\right){x}-179a-439$
375.2-c3	375.2-c	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{10} \cdot 5^{8}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	$2^{2} \cdot 5$	$1$	$4.077978161$	4.162069031	$-\frac{109693837568}{759375} a + \frac{270029745088}{759375}$	$\bigl[a$ , $1$ , $1$ , $11 a - 44$ , $59 a - 163\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(11a-44\right){x}+59a-163$
375.2-c4	375.2-c	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{2} \cdot 5^{4}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.2	$1$	$2^{2}$	$1$	$20.38989080$	4.162069031	$\frac{45398592012032}{15} a + \frac{111203420137408}{15}$	$\bigl[a$ , $-a + 1$ , $1$ , $-329 a - 812$ , $5101 a + 12497\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-329a-812\right){x}+5101a+12497$
375.2-d1	375.2-d	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{5}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.1.2	$1$	$2^{2}$	$5.517065719$	$0.905698896$	2.039935193	$-\frac{81720253739776}{75} a + \frac{66724211524672}{25}$	$\bigl[a$ , $-a + 1$ , $a + 1$ , $-72 a - 232$ , $-582 a - 1712\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-232\right){x}-582a-1712$
375.2-d2	375.2-d	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{5} \cdot 5^{13}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.1.1	$1$	$2^{2} \cdot 5^{2}$	$1.103413143$	$4.528494481$	2.039935193	$-\frac{8297016064}{263671875} a + \frac{155957523008}{87890625}$	$\bigl[a$ , $1$ , $a + 1$ , $8 a - 4$ , $5 a + 4\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-4\right){x}+5a+4$
375.2-d3	375.2-d	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{10} \cdot 5^{8}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.1.1	$1$	$2^{2} \cdot 5^{2}$	$0.551706571$	$9.056988962$	2.039935193	$-\frac{109693837568}{759375} a + \frac{270029745088}{759375}$	$\bigl[a$ , $a + 1$ , $1$ , $-357 a - 874$ , $178 a + 436\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-357a-874\right){x}+178a+436$
375.2-d4	375.2-d	$4$	$10$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{2} \cdot 5^{4}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.1.2	$1$	$2^{2}$	$2.758532859$	$1.811397792$	2.039935193	$\frac{45398592012032}{15} a + \frac{111203420137408}{15}$	$\bigl[a$ , $a + 1$ , $1$ , $308 a - 764$ , $4648 a - 11434\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(308a-764\right){x}+4648a-11434$
375.2-e1	375.2-e	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{5}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$15.83482297$	3.232269705	$-\frac{1075456}{75} a + \frac{877632}{25}$	$\bigl[a$ , $-1$ , $a + 1$ , $13 a - 36$ , $-40 a + 95\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-36\right){x}-40a+95$
375.2-e2	375.2-e	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{2} \cdot 5^{4}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$1$	$15.83482297$	3.232269705	$\frac{143104}{5} a + \frac{1083328}{15}$	$\bigl[a$ , $-a - 1$ , $1$ , $-4 a - 6$ , $-3 a - 7\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-6\right){x}-3a-7$
375.2-f1	375.2-f	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{12} \cdot 5^{7}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4} \cdot 3$	$1$	$1.127613823$	2.762078493	$-\frac{346213168567}{3645} a + \frac{848044778507}{3645}$	$\bigl[1$ , $0$ , $1$ , $-154 a - 387$ , $-4879 a - 11963\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-154a-387\right){x}-4879a-11963$
375.2-f2	375.2-f	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{3} \cdot 5^{7}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2 \cdot 3$	$1$	$9.020910584$	2.762078493	$\frac{16292}{45} a + \frac{13591}{15}$	$\bigl[1$ , $0$ , $1$ , $-19 a - 47$ , $-15 a - 37\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-19a-47\right){x}-15a-37$
375.2-f3	375.2-f	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{6} \cdot 5^{8}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4} \cdot 3$	$1$	$4.510455292$	2.762078493	$\frac{73011154}{675} a + \frac{193909061}{675}$	$\bigl[1$ , $0$ , $1$ , $-229 a - 562$ , $-2969 a - 7273\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-229a-562\right){x}-2969a-7273$
375.2-f4	375.2-f	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{3} \cdot 5^{10}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{3} \cdot 3$	$1$	$2.255227646$	2.762078493	$\frac{349197440831723}{5625} a + \frac{285118523163019}{1875}$	$\bigl[1$ , $a$ , $1$ , $3117 a - 7635$ , $-108499 a + 265765\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(3117a-7635\right){x}-108499a+265765$
375.2-g1	375.2-g	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{12} \cdot 5^{7}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{4} \cdot 3$	$0.060493764$	$7.536433371$	2.233480139	$-\frac{346213168567}{3645} a + \frac{848044778507}{3645}$	$\bigl[a + 1$ , $0$ , $0$ , $185 a - 458$ , $-2125 a + 5223\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(185a-458\right){x}-2125a+5223$
375.2-g2	375.2-g	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3^{3} \cdot 5^{7}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2 \cdot 3$	$0.241975057$	$15.07286674$	2.233480139	$\frac{16292}{45} a + \frac{13591}{15}$	$\bigl[a + 1$ , $0$ , $0$ , $2$ , $-2 a + 5\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+2{x}-2a+5$
375.2-g3	375.2-g	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{6} \cdot 5^{8}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{4} \cdot 3$	$0.120987528$	$15.07286674$	2.233480139	$\frac{73011154}{675} a + \frac{193909061}{675}$	$\bigl[a + 1$ , $0$ , $0$ , $10 a - 33$ , $-30 a + 78\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10a-33\right){x}-30a+78$
375.2-g4	375.2-g	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{3} \cdot 5^{10}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2} \cdot 3$	$0.241975057$	$7.536433371$	2.233480139	$\frac{349197440831723}{5625} a + \frac{285118523163019}{1875}$	$\bigl[a + 1$ , $0$ , $0$ , $-5 a - 168$ , $273 a + 105\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-168\right){x}+273a+105$
375.2-h1	375.2-h	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$- 3 \cdot 5^{5}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.188797424$	$16.84581154$	1.298411572	$-\frac{1075456}{75} a + \frac{877632}{25}$	$\bigl[a$ , $-a - 1$ , $a + 1$ , $-a - 2$ , $a + 2\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+a+2$
375.2-h2	375.2-h	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	375.2	$3 \cdot 5^{3}$	$3^{2} \cdot 5^{4}$	$1.92642$	$(a+3), (-a-1), (-a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.094398712$	$33.69162308$	1.298411572	$\frac{143104}{5} a + \frac{1083328}{15}$	$\bigl[a$ , $-1$ , $1$ , $6 a - 16$ , $-5 a + 12\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-16\right){x}-5a+12$

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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.