Elliptic curve search results

Results (8 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
32.1-a1	32.1-a	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{24} \)	$3.55635$	$(2,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$16$	\( 2 \)	$1$	$6.875185818$	1.643483756	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \)	${y}^2={x}^3-4{x}$
32.1-a2	32.1-a	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \)	$3.55635$	$(2,a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1$	$6.875185818$	1.643483756	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3+{x}$
32.1-b1	32.1-b	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \)	$3.55635$	$(2,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2^{2} \)	$2.064662530$	$6.875185818$	3.393239332	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)	${y}^2={x}^3-{x}$
32.1-b2	32.1-b	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{24} \)	$3.55635$	$(2,a)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$4.129325061$	$6.875185818$	3.393239332	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)	${y}^2={x}^3+4{x}$
32.1-c1	32.1-c	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \cdot 7^{12} \)	$3.55635$	$(2,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2^{2} \)	$2.988881507$	$6.875185818$	4.912178208	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -49\) , \( 0\bigr] \)	${y}^2={x}^3-49{x}$
32.1-c2	32.1-c	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \cdot 5^{12} \)	$3.55635$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1.494440753$	$6.875185818$	4.912178208	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 25\) , \( 0\bigr] \)	${y}^2={x}^3+25{x}$
32.1-d1	32.1-d	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \cdot 5^{12} \)	$3.55635$	$(2,a)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$4.053724506$	$6.875185818$	6.662230381	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -25\) , \( 0\bigr] \)	${y}^2={x}^3-25{x}$
32.1-d2	32.1-d	$4$	$4$	\(\Q(\sqrt{-70}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{12} \cdot 7^{12} \)	$3.55635$	$(2,a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$4.053724506$	$6.875185818$	6.662230381	\( 1728 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 49\) , \( 0\bigr] \)	${y}^2={x}^3+49{x}$

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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.