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
539.1-a1	539.1-a	$3$	$9$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	539.1	\( 7^{2} \cdot 11 \)	\( 7^{4} \cdot 11^{2} \)	$2.47339$	$(-4a-9), (7)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.2	$4$	\( 2^{2} \)	$1$	$0.602881548$	1.679171307	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( 32875 a - 110860\) , \( 5524839 a - 18631313\bigr] \)	${y}^2+{y}={x}^{3}-a{x}^{2}+\left(32875a-110860\right){x}+5524839a-18631313$
539.1-f1	539.1-f	$3$	$9$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	539.1	\( 7^{2} \cdot 11 \)	\( 7^{4} \cdot 11^{2} \)	$2.47339$	$(-4a-9), (7)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 2^{2} \)	$0.745116266$	$21.59210152$	2.489484723	\( -\frac{78843215872}{539} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$

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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.