Elliptic curve search results

Results (4 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
24.1-a4	24.1-a	$6$	$8$	\(\Q(\sqrt{-174}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{8} \)	$5.21790$	$(2,a), (3,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{3} \)	$1$	$7.270694035$	0.551189892	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)	${y}^2={x}^3-{x}^2-24{x}-36$
24.1-b4	24.1-b	$6$	$8$	\(\Q(\sqrt{-174}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{8} \cdot 29^{12} \)	$5.21790$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$12.91360410$	$7.270694035$	7.117848059	\( \frac{1556068}{81} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -4369\) , \( -61697\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-4369{x}-61697$
24.1-c4	24.1-c	$6$	$8$	\(\Q(\sqrt{-174}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{20} \)	$5.21790$	$(2,a), (3,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{4} \)	$1$	$7.270694035$	1.102379784	\( \frac{1556068}{81} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( 576\) , \( -2106\bigr] \)	${y}^2+a{x}{y}={x}^3+576{x}-2106$
24.1-d4	24.1-d	$6$	$8$	\(\Q(\sqrt{-174}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{8} \)	$5.21790$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{5} \)	$11.44080444$	$7.270694035$	12.61211153	\( \frac{1556068}{81} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 683\) , \( -2719\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+683{x}-2719$

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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.