Elliptic curve search results

Results (5 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
320.1-a5	320.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	320.1	\( 2^{6} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$0.84511$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$1$	$35.25568626$	0.985426388	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)	${y}^2={x}^{3}-2{x}+1$
1280.1-a5	1280.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2 \)	$1$	$23.97511185$	1.340249496	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 \phi - 4\) , \( -2 \phi + 3\bigr] \)	${y}^2={x}^{3}+\left(2\phi-4\right){x}-2\phi+3$
1280.1-i5	1280.1-i	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$0.933393502$	$16.30392283$	1.701421401	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2={x}^{3}-2{x}-1$
1280.1-j5	1280.1-j	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2 \)	$1$	$23.97511185$	1.340249496	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 \phi - 4\) , \( 2 \phi - 3\bigr] \)	${y}^2={x}^{3}+\left(2\phi-4\right){x}+2\phi-3$
1600.1-a5	1600.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1600.1	\( 2^{6} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{8} \)	$1.26373$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$7.291335953$	1.630392283	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -10 \phi - 10\) , \( -20 \phi - 15\bigr] \)	${y}^2={x}^{3}+\left(-10\phi-10\right){x}-20\phi-15$

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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.