Elliptic curve search results

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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
729.1-c2	729.1-c	$2$	$3$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{6} \)	$1.03826$	$(3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B.1.1	$1$	\( 1 \)	$1$	$25.72771921$	1.278420645	\( -72927 a + 119583 \)	\( \bigl[1\) , \( -1\) , \( \phi\) , \( \phi\) , \( -\phi\bigr] \)	${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}+\phi{x}-\phi$
729.1-g2	729.1-g	$2$	$3$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{18} \)	$1.03826$	$(3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B.1.2	$1$	\( 3 \)	$0.093656179$	$4.848975052$	1.218576037	\( -72927 a + 119583 \)	\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( 13 \phi - 2\) , \( 6 \phi - 6\bigr] \)	${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(13\phi-2\right){x}+6\phi-6$

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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.