Elliptic curves over \(\Q(\sqrt{-22}) \) of conductor 32.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 88

Note: The completeness Only modular elliptic curves are included

Results (8 matches)

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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
32.1-a1	32.1-a	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{24} \)	$1.99373$	$(2,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1$	$6.875185818$	0.732897270	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \)	${y}^2={x}^3-4{x}$
32.1-a2	32.1-a	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \)	$1.99373$	$(2,a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1$	$6.875185818$	0.732897270	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3+{x}$
32.1-a3	32.1-a	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.99373$	$(2,a)$	0	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1$	$6.875185818$	0.732897270	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 8\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+15{x}+8$
32.1-a4	32.1-a	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.99373$	$(2,a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1$	$6.875185818$	0.732897270	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( -1\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2+4{x}-1$
32.1-b1	32.1-b	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \)	$1.99373$	$(2,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{2} \)	$4.253144970$	$6.875185818$	3.117118340	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)	${y}^2={x}^3-{x}$
32.1-b2	32.1-b	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{24} \)	$1.99373$	$(2,a)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	\( 2 \)	$8.506289940$	$6.875185818$	3.117118340	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)	${y}^2={x}^3+4{x}$
32.1-b3	32.1-b	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{18} \)	$1.99373$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	\( 2 \)	$2.126572485$	$6.875185818$	3.117118340	\( 287496 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \)	${y}^2={x}^3-11{x}-14$
32.1-b4	32.1-b	$4$	$4$	\(\Q(\sqrt{-22}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{18} \)	$1.99373$	$(2,a)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	\( 2 \)	$8.506289940$	$6.875185818$	3.117118340	\( 287496 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \)	${y}^2={x}^3-11{x}+14$

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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.