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-a3	32.1-a	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \cdot 5^{12} \)	$4.45813$	$(2,a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1$	$6.875185818$	1.311046494	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 257\) , \( 42\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+257{x}+42$
32.1-a4	32.1-a	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \cdot 5^{12} \)	$4.45813$	$(2,a)$	0	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$1$	$6.875185818$	1.311046494	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 202\) , \( -423\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2+202{x}-423$
32.1-b3	32.1-b	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{18} \)	$4.45813$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$4.693397835$	$6.875185818$	3.076631389	\( 287496 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \)	${y}^2={x}^3-11{x}-14$
32.1-b4	32.1-b	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{18} \)	$4.45813$	$(2,a)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$4.693397835$	$6.875185818$	3.076631389	\( 287496 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \)	${y}^2={x}^3-11{x}+14$
32.1-c3	32.1-c	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \cdot 11^{12} \)	$4.45813$	$(2,a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$8.078773048$	$6.875185818$	10.59164708	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -62\) , \( 4633\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-62{x}+4633$
32.1-c4	32.1-c	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \cdot 11^{12} \)	$4.45813$	$(2,a)$	$2$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$8.078773048$	$6.875185818$	10.59164708	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( 2\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-7{x}+2$
32.1-d3	32.1-d	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$4.45813$	$(2,a)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$4$	\( 2 \)	$9.943524887$	$6.875185818$	6.518211722	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 323\) , \( -802\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+323{x}-802$
32.1-d4	32.1-d	$4$	$4$	\(\Q(\sqrt{-110}) \)	$2$	$[0, 1]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$4.45813$	$(2,a)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$9.943524887$	$6.875185818$	6.518211722	\( 287496 \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 268\) , \( -833\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2+268{x}-833$

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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.