Elliptic curves over \(\Q(\sqrt{-1671}) \) of conductor 4.2

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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
4.2-a1	4.2-a	$1$	$1$	\(\Q(\sqrt{-1671}) \)	$2$	$[0, 1]$	4.2	\( 2^{2} \)	\( 2^{6} \cdot 107^{12} \)	$5.16585$	$(2,a), (2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$1.559822010$	$19.45262438$	2.969101276	\( \frac{123}{32} a + \frac{51895}{32} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -115 a + 5001\) , \( 3501 a - 7361\bigr] \)	${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-115a+5001\right){x}+3501a-7361$
4.2-b1	4.2-b	$1$	$1$	\(\Q(\sqrt{-1671}) \)	$2$	$[0, 1]$	4.2	\( 2^{2} \)	\( 2^{6} \cdot 7^{12} \)	$5.16585$	$(2,a), (2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$4$	\( 5 \)	$1$	$19.45262438$	9.517436144	\( -\frac{123}{32} a + \frac{26009}{16} \)	\( \bigl[1\) , \( -a\) , \( 1\) , \( -a - 142\) , \( 17 a - 152\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-a-142\right){x}+17a-152$
4.2-c1	4.2-c	$1$	$1$	\(\Q(\sqrt{-1671}) \)	$2$	$[0, 1]$	4.2	\( 2^{2} \)	\( 2^{6} \cdot 107^{12} \)	$5.16585$	$(2,a), (2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$1.559822010$	$19.45262438$	2.969101276	\( -\frac{123}{32} a + \frac{26009}{16} \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 117 a + 4884\) , \( -3617 a - 8745\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(117a+4884\right){x}-3617a-8745$
4.2-d1	4.2-d	$1$	$1$	\(\Q(\sqrt{-1671}) \)	$2$	$[0, 1]$	4.2	\( 2^{2} \)	\( 2^{6} \cdot 7^{12} \)	$5.16585$	$(2,a), (2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$4$	\( 5 \)	$1$	$19.45262438$	9.517436144	\( \frac{123}{32} a + \frac{51895}{32} \)	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( a - 143\) , \( -17 a - 135\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(a-143\right){x}-17a-135$

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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.