Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 65536.1

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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-a1	65536.1-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{18} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$0.480125797$	$4.486587907$	2.487371141	\( 8000 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \)	${y}^2={x}^{3}+{x}^{2}-3{x}+1$
65536.1-a2	65536.1-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{30} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$0.960251595$	$2.243293953$	2.487371141	\( 8000 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( -21\bigr] \)	${y}^2={x}^{3}+{x}^{2}-13{x}-21$
65536.1-c1	65536.1-c	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{18} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$0.608709031$	$4.861490513$	3.417028151	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \)	${y}^2={x}^{3}-2{x}$
65536.1-c2	65536.1-c	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{30} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.217418063$	$2.430745256$	3.417028151	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8\) , \( 0\bigr] \)	${y}^2={x}^{3}+8{x}$
65536.1-d1	65536.1-d	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{30} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.429482697$	$2.430745256$	4.012247529	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a\) , \( 0\bigr] \)	${y}^2={x}^{3}+8a{x}$
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	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a\) , \( 0\bigr] \)	${y}^2={x}^{3}-2a{x}$
65536.1-f1	65536.1-f	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{18} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.056438687$	$4.486587907$	5.473055434	\( 8000 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a\) , \( -1\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3a{x}-1$
65536.1-f2	65536.1-f	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65536.1	\( 2^{16} \)	\( 2^{30} \)	$2.47639$	$(2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$2.112877375$	$2.243293953$	5.473055434	\( 8000 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 13 a\) , \( 21\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+13a{x}+21$

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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.