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
32.1-d3	32.1-d	$4$	$4$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.59045$	$(-a+4)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.067060424$	$13.75037163$	1.960692265	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -330 a - 1228\) , \( -6788 a - 25395\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-330a-1228\right){x}-6788a-25395$
32.1-d4	32.1-d	$4$	$4$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.59045$	$(-a+4)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.067060424$	$55.00148654$	1.960692265	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -330 a - 1235\) , \( 5798 a + 21694\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-330a-1235\right){x}+5798a+21694$
32.1-e3	32.1-e	$4$	$4$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.59045$	$(-a+4)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.494440753$	$13.75037163$	2.745991098	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -6\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}-6$
32.1-e4	32.1-e	$4$	$4$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	32.1	\( 2^{5} \)	\( 2^{6} \)	$1.59045$	$(-a+4)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	\( 2 \)	$1.494440753$	$55.00148654$	2.745991098	\( 287496 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( 1\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+4{x}+1$

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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.