Elliptic curves over Q(−7)\Q(\sqrt{-7}) of conductor 10404.2

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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
10404.2-a1	10404.2-a	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{2} \cdot 3^{8} \cdot 17^{4}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$0.286507785$	$2.302301329$	1.994525346	$\frac{46268279}{46818}$	$\bigl[1$ , $1$ , $0$ , $8$ , $10\bigr]$	${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$
10404.2-a2	10404.2-a	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{4} \cdot 3^{4} \cdot 17^{2}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$0.143253892$	$4.604602658$	1.994525346	$\frac{1771561}{612}$	$\bigl[1$ , $1$ , $0$ , $-2$ , $0\bigr]$	${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$
10404.2-b1	10404.2-b	$4$	$6$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{6} \cdot 3^{24} \cdot 17^{4}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$5.231471366$	$0.415867934$	2.192799889	$-\frac{1107111813625}{1228691592}$	$\bigl[1$ , $0$ , $1$ , $-216$ , $2062\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$
10404.2-b2	10404.2-b	$4$	$6$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{18} \cdot 3^{8} \cdot 17^{12}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3} \cdot 3$	$1.743823788$	$0.138622644$	2.192799889	$\frac{655215969476375}{1001033261568}$	$\bigl[1$ , $0$ , $1$ , $1809$ , $-37790\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$
10404.2-b3	10404.2-b	$4$	$6$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{36} \cdot 3^{4} \cdot 17^{6}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3} \cdot 3$	$0.871911894$	$0.277245289$	2.192799889	$\frac{46753267515625}{11591221248}$	$\bigl[1$ , $0$ , $1$ , $-751$ , $-6046\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-751{x}-6046$
10404.2-b4	10404.2-b	$4$	$6$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{12} \cdot 3^{12} \cdot 17^{2}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$2.615735683$	$0.831735869$	2.192799889	$\frac{1845026709625}{793152}$	$\bigl[1$ , $0$ , $1$ , $-256$ , $1550\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-256{x}+1550$
10404.2-c1	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{2} \cdot 3^{4} \cdot 17^{16}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	$2^{4}$	$1.755122514$	$0.183754147$	7.801453798	$-\frac{491411892194497}{125563633938}$	$\bigl[1$ , $0$ , $0$ , $-1644$ , $-30942\bigr]$	${y}^2+{x}{y}={x}^{3}-1644{x}-30942$
10404.2-c2	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{4} \cdot 3^{32} \cdot 17^{2}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{6}$	$3.510245028$	$0.367508294$	7.801453798	$\frac{1276229915423}{2927177028}$	$\bigl[1$ , $0$ , $0$ , $226$ , $-2232\bigr]$	${y}^2+{x}{y}={x}^{3}+226{x}-2232$
10404.2-c3	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{8} \cdot 3^{16} \cdot 17^{4}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{8}$	$1.755122514$	$0.735016588$	7.801453798	$\frac{163936758817}{30338064}$	$\bigl[1$ , $0$ , $0$ , $-114$ , $-396\bigr]$	${y}^2+{x}{y}={x}^{3}-114{x}-396$
10404.2-c4	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{16} \cdot 3^{8} \cdot 17^{2}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{8}$	$0.877561257$	$1.470033177$	7.801453798	$\frac{4354703137}{352512}$	$\bigl[1$ , $0$ , $0$ , $-34$ , $68\bigr]$	${y}^2+{x}{y}={x}^{3}-34{x}+68$
10404.2-c5	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{4} \cdot 3^{8} \cdot 17^{8}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2^{6}$	$0.877561257$	$0.367508294$	7.801453798	$\frac{576615941610337}{27060804}$	$\bigl[1$ , $0$ , $0$ , $-1734$ , $-27936\bigr]$	${y}^2+{x}{y}={x}^{3}-1734{x}-27936$
10404.2-c6	10404.2-c	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	10404.2	$2^{2} \cdot 3^{2} \cdot 17^{2}$	$2^{2} \cdot 3^{4} \cdot 17^{4}$	$2.38774$	$(a), (-a+1), (3), (17)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$16$	$2^{2}$	$1.755122514$	$0.183754147$	7.801453798	$\frac{2361739090258884097}{5202}$	$\bigl[1$ , $0$ , $0$ , $-27744$ , $-1781010\bigr]$	${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$

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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.