Elliptic curve search results

Results (7 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
65536.1-d2	65536.1-d	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{18} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$0.714741348$	$4.861490513$	4.012247529	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a\) , \( 0\bigr] \)	${y}^2={x}^{3}-2a{x}$
4096.1-CMc1	4096.1-CMc	$1$	$1$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	4096.1	\( 2^{12} \)	\( 2^{18} \)	$1.42974$	$(a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓	✓		✓			$1$	\( 2 \)	$1$	$4.861490513$	2.430745256	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+2{x}$
1024.1-b2	1024.1-b	$4$	$4$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1024.1	\( 2^{10} \)	\( 2^{18} \)	$1.42974$	$(a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	\( 2^{2} \)	$1.217418063$	$4.861490513$	2.092493851	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+2{x}$
1024.1-k3	1024.1-k	$8$	$16$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( 2^{18} \)	$1.42974$	$(a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2^{2} \)	$0.304354515$	$9.722981027$	2.092493851	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+2{x}$
4096.1-j2	4096.1-j	$2$	$2$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	4096.1	\( 2^{12} \)	\( 2^{18} \)	$2.47639$	$(a+1)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2^{2} \)	$0.714741348$	$9.722981027$	4.012247529	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2={x}^{3}+2{x}$
256.1-e7	256.1-e	$8$	$16$	\(\Q(\zeta_{16})^+\)	$4$	$[4, 0]$	256.1	\( 2^{8} \)	\( 2^{12} \)	$8.08786$	$(a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 1 \)	$0.304354515$	$378.1454402$	2.543159752	\( 1728 \)	\( \bigl[a^{3} - 2 a\) , \( a^{2} - 3\) , \( a^{3} - 2 a\) , \( -a^{2} + 2\) , \( -1\bigr] \)	${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+2\right){x}-1$
32.1-a5	32.1-a	$8$	$16$	\(\Q(\sqrt{4 + \sqrt{2}})\)	$4$	$[4, 0]$	32.1	\( 2^{5} \)	\( 2^{12} \)	$16.50047$	$(a-2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2^{2} \)	$0.304354515$	$378.1454402$	3.844896143	\( 1728 \)	\( \bigl[a^{3} - 4 a\) , \( a^{2} - 3\) , \( 0\) , \( 3 a^{2} - 7\) , \( 2 a^{2} - 5\bigr] \)	${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{2}-7\right){x}+2a^{2}-5$

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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.