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
72.1-e2	72.1-e	$6$	$8$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	72.1	\( 2^{3} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{2} \)	$1.64627$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1$	$18.60223895$	2.941272233	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \)	${y}^2={x}^{3}+{x}^{2}+3{x}+3$
72.1-f2	72.1-f	$6$	$8$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	72.1	\( 2^{3} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{2} \)	$1.64627$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2 \)	$2.249823046$	$18.60223895$	1.654335513	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^{3}-{x}^{2}+{x}$
144.1-c2	144.1-c	$6$	$8$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{2} \)	$1.95776$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 1 \)	$4.274166887$	$11.36701703$	3.840944173	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^{3}+{x}^{2}+{x}$
144.1-d2	144.1-d	$6$	$8$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{2} \)	$1.95776$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 1 \)	$2.993933771$	$11.36701703$	2.690473437	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \)	${y}^2={x}^{3}-{x}^{2}+3{x}-3$

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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.