Elliptic curve search results

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
16384.1-a2	16384.1-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{26} \)	$1.75107$	$(2)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$0.176493078$	$2.772397005$	2.260020919	\( 10976 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -9\) , \( 7\bigr] \)	${y}^2={x}^{3}+{x}^{2}-9{x}+7$
16384.1-b2	16384.1-b	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{14} \)	$1.75107$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 1 \)	$1$	$5.544794010$	1.600644157	\( 10976 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \)	${y}^2={x}^{3}+{x}^{2}-2{x}-2$
16384.1-g2	16384.1-g	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{14} \)	$1.75107$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 1 \)	$1$	$5.544794010$	1.600644157	\( 10976 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 2\) , \( 2\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2$
16384.1-h2	16384.1-h	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	16384.1	\( 2^{14} \)	\( 2^{26} \)	$1.75107$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$2.772397005$	3.201288314	\( 10976 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 9 a\) , \( -7\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+9a{x}-7$
147456.1-c2	147456.1-c	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	147456.1	\( 2^{14} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{6} \)	$3.03295$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$1$	$3.201288314$	1.848264670	\( 10976 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a\) , \( -12 a + 6\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}-6a{x}-12a+6$
147456.1-d2	147456.1-d	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	147456.1	\( 2^{14} \cdot 3^{2} \)	\( 2^{26} \cdot 3^{6} \)	$3.03295$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2^{2} \)	$1.338070784$	$1.600644157$	4.946217913	\( 10976 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -27 a\) , \( -42 a + 21\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-27a{x}-42a+21$
147456.1-bs2	147456.1-bs	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	147456.1	\( 2^{14} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{6} \)	$3.03295$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$1$	$3.201288314$	1.848264670	\( 10976 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 7\) , \( 5 a + 1\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-7\right){x}+5a+1$
147456.1-bt2	147456.1-bt	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	147456.1	\( 2^{14} \cdot 3^{2} \)	\( 2^{26} \cdot 3^{6} \)	$3.03295$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2^{2} \)	$1.338070784$	$1.600644157$	4.946217913	\( 10976 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -27 a\) , \( 42 a - 21\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}-27a{x}+42a-21$

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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.