Elliptic curves over Q(−11)\Q(\sqrt{-11}) of conductor 22275.1

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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
22275.1-a1	22275.1-a	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{12} \cdot 5^{8} \cdot 11^{3}$	$3.62067$	$(-a), (-a-1), (-2a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	$1$	$1$	$0.821696092$	0.495501387	$\frac{53585}{121} a + \frac{497055}{121}$	$\bigl[1$ , $a - 1$ , $0$ , $29 a + 57$ , $-66 a + 198\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a+57\right){x}-66a+198$
22275.1-a2	22275.1-a	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{4} \cdot 5^{8} \cdot 11$	$3.62067$	$(-a), (-a-1), (-2a+1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	$3$	$1$	$2.465088277$	0.495501387	$-\frac{32585}{11} a + \frac{82320}{11}$	$\bigl[1$ , $a - 1$ , $0$ , $-6 a - 3$ , $-9 a + 10\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-3\right){x}-9a+10$
22275.1-b1	22275.1-b	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{6} \cdot 5^{10} \cdot 11^{15}$	$3.62067$	$(-a), (-a-1), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	$2 \cdot 3$	$6.185941732$	$0.098745448$	4.420158156	$\frac{288322789502659}{133974300625} a - \frac{241975044280128}{133974300625}$	$\bigl[1$ , $-a - 1$ , $a$ , $2612 a - 4923$ , $-96076 a + 130747\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2612a-4923\right){x}-96076a+130747$
22275.1-b2	22275.1-b	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{10} \cdot 5^{18} \cdot 11^{5}$	$3.62067$	$(-a), (-a-1), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	$2 \cdot 3$	$18.55782519$	$0.032915149$	4.420158156	$-\frac{4761132976229511855379}{324951171875} a + \frac{19904467562618343492243}{324951171875}$	$\bigl[1$ , $-a - 1$ , $a$ , $205287 a - 422373$ , $-69676884 a + 76785094\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(205287a-422373\right){x}-69676884a+76785094$
22275.1-c1	22275.1-c	$1$	$1$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{12} \cdot 5^{6} \cdot 11$	$3.62067$	$(-a), (-a-1), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$2$	$0.592815284$	$1.590343894$	2.274071327	$-\frac{6346}{11} a - \frac{36735}{11}$	$\bigl[a + 1$ , $a - 1$ , $a$ , $10 a + 3$ , $a - 67\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a+3\right){x}+a-67$
22275.1-d1	22275.1-d	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{12} \cdot 5^{2} \cdot 11^{3}$	$3.62067$	$(-a), (-a-1), (-2a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	$3$	$1$	$1.837368319$	3.323924355	$\frac{53585}{121} a + \frac{497055}{121}$	$\bigl[a + 1$ , $-a - 1$ , $a$ , $-10 a + 15$ , $4 a - 30\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+15\right){x}+4a-30$
22275.1-d2	22275.1-d	$2$	$3$	$\Q(\sqrt{-11})$	$2$	$[0, 1]$	22275.1	$3^{4} \cdot 5^{2} \cdot 11$	$3^{4} \cdot 5^{2} \cdot 11$	$3.62067$	$(-a), (-a-1), (-2a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	$1$	$1$	$5.512104959$	3.323924355	$-\frac{32585}{11} a + \frac{82320}{11}$	$\bigl[a + 1$ , $-a - 1$ , $a$ , $0$ , $1\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+1$

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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.