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
128.1-a2	128.1-a	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{14} \)	$1.90095$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$0.763284993$	$22.17917604$	2.676715022	\( 10976 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 41\) , \( 61 a - 194\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(14a-41\right){x}+61a-194$
128.1-b2	128.1-b	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{14} \)	$1.90095$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$0.763284993$	$22.17917604$	2.676715022	\( 10976 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a - 41\) , \( -61 a - 194\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-14a-41\right){x}-61a-194$
128.1-c2	128.1-c	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{26} \)	$1.90095$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$1$	$22.17917604$	1.753417822	\( 10976 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -56 a - 174\) , \( -314 a - 992\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-56a-174\right){x}-314a-992$
128.1-d2	128.1-d	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	128.1	\( 2^{7} \)	\( 2^{26} \)	$1.90095$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	\( 2 \)	$1$	$22.17917604$	1.753417822	\( 10976 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( 56 a - 174\) , \( 314 a - 992\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(56a-174\right){x}+314a-992$
256.1-a2	256.1-a	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{26} \)	$2.26063$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$1.221085282$	$15.09590514$	5.829148982	\( 10976 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( -7\bigr] \)	${y}^2={x}^{3}-{x}^{2}-9{x}-7$
256.1-c2	256.1-c	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{26} \)	$2.26063$	$(2,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$0.113076171$	$32.58604536$	2.330412212	\( 10976 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -9\) , \( 7\bigr] \)	${y}^2={x}^{3}+{x}^{2}-9{x}+7$
256.1-d2	256.1-d	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{14} \)	$2.26063$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$32.58604536$	5.152306164	\( 10976 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)	${y}^2={x}^{3}-{x}^{2}-2{x}+2$
256.1-f2	256.1-f	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	256.1	\( 2^{8} \)	\( 2^{14} \)	$2.26063$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$2$	2B	$1$	\( 2^{2} \)	$0.421511071$	$15.09590514$	2.012186100	\( 10976 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \)	${y}^2={x}^{3}+{x}^{2}-2{x}-2$

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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.