Elliptic curves over Q(6)\Q(\sqrt{6}) of conductor 392.1

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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
392.1-a1	392.1-a	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{8} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$22.75712104$	4.645277881	$-\frac{4}{7}$	$\bigl[a$ , $-1$ , $a$ , $-3$ , $-1\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-3{x}-1$
392.1-a2	392.1-a	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{4}$	$1.94790$	$(-a+2), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$22.75712104$	4.645277881	$\frac{3543122}{49}$	$\bigl[a$ , $-1$ , $a$ , $-13$ , $9\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-13{x}+9$
392.1-b1	392.1-b	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{8} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1.747807462$	$7.189921948$	2.565146328	$-\frac{4}{7}$	$\bigl[a$ , $-a - 1$ , $0$ , $-2 a - 2$ , $-100 a - 244\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-2\right){x}-100a-244$
392.1-b2	392.1-b	$2$	$2$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{4}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$0.873903731$	$7.189921948$	2.565146328	$\frac{3543122}{49}$	$\bigl[a$ , $a - 1$ , $0$ , $202 a - 492$ , $2280 a - 5584\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(202a-492\right){x}+2280a-5584$
392.1-c1	392.1-c	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{4} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	$2$	$1$	$24.47471212$	2.497939845	$\frac{432}{7}$	$\bigl[a$ , $0$ , $a$ , $5 a + 10$ , $52 a + 126\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(5a+10\right){x}+52a+126$
392.1-c2	392.1-c	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{8}$	$1.94790$	$(-a+2), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$6.118678030$	2.497939845	$\frac{11090466}{2401}$	$\bigl[a$ , $0$ , $a$ , $-295 a - 725$ , $-3563 a - 8729\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-295a-725\right){x}-3563a-8729$
392.1-c3	392.1-c	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{8} \cdot 7^{4}$	$1.94790$	$(-a+2), (7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$1$	$24.47471212$	2.497939845	$\frac{740772}{49}$	$\bigl[a$ , $0$ , $a$ , $95 a - 235$ , $-695 a + 1701\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(95a-235\right){x}-695a+1701$
392.1-c4	392.1-c	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1$	$24.47471212$	2.497939845	$\frac{1443468546}{7}$	$\bigl[a$ , $0$ , $a$ , $-1495 a - 3665$ , $48505 a + 118811\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-1495a-3665\right){x}+48505a+118811$
392.1-d1	392.1-d	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{4} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1.069108576$	$10.54517411$	2.301282567	$\frac{432}{7}$	$\bigl[a$ , $0$ , $0$ , $1$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}$
392.1-d2	392.1-d	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{8}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1.069108576$	$10.54517411$	2.301282567	$\frac{11090466}{2401}$	$\bigl[a$ , $0$ , $0$ , $-14$ , $10\bigr]$	${y}^2+a{x}{y}={x}^{3}-14{x}+10$
392.1-d3	392.1-d	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{8} \cdot 7^{4}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{2}$	$2.138217153$	$10.54517411$	2.301282567	$\frac{740772}{49}$	$\bigl[a$ , $0$ , $0$ , $-4$ , $-6\bigr]$	${y}^2+a{x}{y}={x}^{3}-4{x}-6$
392.1-d4	392.1-d	$4$	$4$	$\Q(\sqrt{6})$	$2$	$[2, 0]$	392.1	$2^{3} \cdot 7^{2}$	$2^{10} \cdot 7^{2}$	$1.94790$	$(-a+2), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$4.276434307$	$2.636293528$	2.301282567	$\frac{1443468546}{7}$	$\bigl[a$ , $0$ , $0$ , $-74$ , $-286\bigr]$	${y}^2+a{x}{y}={x}^{3}-74{x}-286$

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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.