Elliptic curves over \(\Q(\sqrt{-2019}) \)

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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
3.1-a1	3.1-a	$1$	$1$	\(\Q(\sqrt{-2019}) \)	$2$	$[0, 1]$	3.1	\( 3 \)	\( 3^{18} \cdot 13^{12} \)	$5.28429$	$(3,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Cn	$1$	\( 2 \cdot 3^{2} \)	$1.210811334$	$4.473174323$	8.678739206	\( -\frac{575930368}{19683} \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( -17 a - 3063\) , \( 434 a - 64170\bigr] \)	${y}^2+{y}={x}^3-a{x}^2+\left(-17a-3063\right){x}+434a-64170$
3.1-b1	3.1-b	$1$	$1$	\(\Q(\sqrt{-2019}) \)	$2$	$[0, 1]$	3.1	\( 3 \)	\( 3^{18} \cdot 13^{12} \)	$5.28429$	$(3,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2Cn, 3Cn	$1$	\( 2 \cdot 3^{2} \)	$1.210811334$	$4.473174323$	8.678739206	\( -\frac{575930368}{19683} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 17 a - 3080\) , \( -434 a - 63736\bigr] \)	${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(17a-3080\right){x}-434a-63736$

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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.