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
86436.3-h1	86436.3-h	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	86436.3	\( 2^{2} \cdot 3^{2} \cdot 7^{4} \)	\( 2^{6} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B[2]	$1$	\( 2 \cdot 3 \)	$0.213735627$	$1.498465456$	4.437866884	\( -\frac{67645179}{8} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-93{x}-323$
15876.2-d1	15876.2-d	$2$	$3$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	15876.2	\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{6} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(a), (-a+1), (-2a+1), (3)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1	$1$	\( 2 \cdot 3 \)	$1.646058679$	$1.498465456$	2.486060889	\( -\frac{67645179}{8} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-93{x}-323$
882.1-b1	882.1-b	$2$	$3$	\(\Q(\sqrt{-21}) \)	$2$	$[0, 1]$	882.1	\( 2 \cdot 3^{2} \cdot 7^{2} \)	\( 2^{6} \cdot 3^{6} \cdot 7^{4} \)	$4.46319$	$(2,a+1), (3,a), (7,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$4$	\( 2^{2} \)	$1$	$1.498465456$	5.231871529	\( -\frac{67645179}{8} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-93{x}-323$
1764.1-b1	1764.1-b	$2$	$3$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1764.1	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{6} \cdot 3^{6} \cdot 7^{4} \)	$2.65383$	$(-a+2), (a+3), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.2	$1$	\( 2^{2} \cdot 3^{2} \)	$1$	$0.590274639$	4.637105514	\( -\frac{67645179}{8} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-93{x}-323$

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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.