Elliptic curves over \(\Q(\sqrt{-2163}) \)

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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
7.1-a1	7.1-a	$1$	$1$	\(\Q(\sqrt{-2163}) \)	$2$	$[0, 1]$	7.1	\( 7 \)	\( 7^{6} \cdot 17^{12} \)	$6.75992$	$(7,a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Nn	$1$	\( 2 \cdot 3 \)	$1$	$8.591165428$	1.108345270	\( -\frac{13824000}{343} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -55 a + 700\) , \( -55 a + 21580\bigr] \)	${y}^2+{y}={x}^3+\left(-55a+700\right){x}-55a+21580$
7.1-b1	7.1-b	$1$	$1$	\(\Q(\sqrt{-2163}) \)	$2$	$[0, 1]$	7.1	\( 7 \)	\( 7^{6} \cdot 17^{12} \)	$6.75992$	$(7,a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Nn	$1$	\( 2 \cdot 3 \)	$1$	$8.591165428$	1.108345270	\( -\frac{13824000}{343} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 55 a + 645\) , \( 55 a + 21525\bigr] \)	${y}^2+{y}={x}^3+\left(55a+645\right){x}+55a+21525$
7.1-c1	7.1-c	$1$	$1$	\(\Q(\sqrt{-2163}) \)	$2$	$[0, 1]$	7.1	\( 7 \)	\( 7^{6} \cdot 11^{12} \)	$6.75992$	$(7,a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Nn	$1$	\( 2 \cdot 3 \)	$1$	$8.591165428$	1.108345270	\( -\frac{13824000}{343} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 25 a - 180\) , \( 235 a + 1968\bigr] \)	${y}^2+{y}={x}^3+\left(25a-180\right){x}+235a+1968$
7.1-d1	7.1-d	$1$	$1$	\(\Q(\sqrt{-2163}) \)	$2$	$[0, 1]$	7.1	\( 7 \)	\( 7^{6} \cdot 11^{12} \)	$6.75992$	$(7,a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Nn	$1$	\( 2 \cdot 3 \)	$1$	$8.591165428$	1.108345270	\( -\frac{13824000}{343} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -25 a - 155\) , \( -235 a + 2203\bigr] \)	${y}^2+{y}={x}^3+\left(-25a-155\right){x}-235a+2203$

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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.