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
2401.3-a2	2401.3-a	$4$	$14$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	2401.3	\( 7^{4} \)	\( 7^{18} \)	$2.72655$	$(-a-1), (a-2)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓	✓		✓	$7$	7B.1.2	$1$	\( 2^{2} \)	$4.528181219$	$0.706357800$	2.935159696	\( -3375 \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -107\) , \( 552\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-107{x}+552$
49.1-a2	49.1-a	$4$	$14$	\(\Q(\sqrt{-399}) \)	$2$	$[0, 1]$	49.1	\( 7^{2} \)	\( 3^{12} \cdot 7^{6} \)	$4.72252$	$(7,a+3)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓	✓		✓	$7$	7B.6.2	$1$	\( 2^{2} \)	$1.984975936$	$4.944504600$	3.930805641	\( -3375 \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -20\) , \( 46\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-20{x}+46$
49.1-a2	49.1-a	$4$	$14$	\(\Q(\sqrt{-133}) \)	$2$	$[0, 1]$	49.1	\( 7^{2} \)	\( 7^{6} \)	$5.45310$	$(7,a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓	✓		✓	$7$	7B.6.2	$1$	\( 2 \)	$7.817108783$	$9.889009200$	6.703060143	\( -3375 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 411\) , \( -1184\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+411{x}-1184$
49.1-c1	49.1-c	$4$	$14$	\(\Q(\sqrt{133}) \)	$2$	$[2, 0]$	49.1	\( 7^{2} \)	\( 7^{6} \)	$2.72655$	$(-3a+19)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓	✓		✓	$7$	7B.1.5	$1$	\( 2^{2} \)	$4.528181219$	$3.737694151$	2.935159696	\( -3375 \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$

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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.