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-a6	320.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	320.1	\( 2^{6} \cdot 5 \)	\( 2^{20} \cdot 5^{2} \)	$0.84511$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$2.203480391$	0.985426388	\( \frac{132304644}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \)	${y}^2={x}^{3}-107{x}-426$
1280.1-a6	1280.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{20} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$5.993777963$	1.340249496	\( \frac{132304644}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107 \phi - 107\) , \( 852 \phi + 426\bigr] \)	${y}^2={x}^{3}+\left(-107\phi-107\right){x}+852\phi+426$
1280.1-i6	1280.1-i	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{20} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.933393502$	$16.30392283$	1.701421401	\( \frac{132304644}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \)	${y}^2={x}^{3}-107{x}+426$
1280.1-j6	1280.1-j	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( 2^{20} \cdot 5^{2} \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$5.993777963$	1.340249496	\( \frac{132304644}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107 \phi - 107\) , \( -852 \phi - 426\bigr] \)	${y}^2={x}^{3}+\left(-107\phi-107\right){x}-852\phi-426$
1600.1-a6	1600.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1600.1	\( 2^{6} \cdot 5^{2} \)	\( 2^{20} \cdot 5^{8} \)	$1.26373$	$(-2a+1), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$7.291335953$	1.630392283	\( \frac{132304644}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -535 \phi - 535\) , \( 8520 \phi + 6390\bigr] \)	${y}^2={x}^{3}+\left(-535\phi-535\right){x}+8520\phi+6390$

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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.