Elliptic curves over $\Q$ of conductor 539

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (9 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
539.a1	539d3	539.a	539d	$3$	$25$	\( 7^{2} \cdot 11 \)	\( - 7^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$3850$	$1200$	$37$	$0.555680735$	$1$		$0$	$1800$	$1.469664$	$-52893159101157376/11$	$1.09296$	$7.97850$	$[0, 1, 1, -383196, 91174234]$	\(y^2+y=x^3+x^2-383196x+91174234\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 35.24.0-5.a.2.2, 110.24.1.?, $\ldots$	$[(1429/2, 45/2)]$	$1$
539.a2	539d2	539.a	539d	$3$	$25$	\( 7^{2} \cdot 11 \)	\( - 7^{6} \cdot 11^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$3850$	$1200$	$37$	$0.111136147$	$1$		$6$	$360$	$0.664946$	$-122023936/161051$	$1.01300$	$5.00551$	$[0, 1, 1, -506, 7774]$	\(y^2+y=x^3+x^2-506x+7774\)	5.60.0.a.1, 22.2.0.a.1, 35.120.0-5.a.1.2, 110.120.5.?, 275.300.12.?, $\ldots$	$[(44, 269)]$	$1$
539.a3	539d1	539.a	539d	$3$	$25$	\( 7^{2} \cdot 11 \)	\( - 7^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$3850$	$1200$	$37$	$0.555680735$	$1$		$4$	$72$	$-0.139774$	$-4096/11$	$0.82546$	$3.45377$	$[0, 1, 1, -16, -66]$	\(y^2+y=x^3+x^2-16x-66\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 35.24.0-5.a.1.2, 110.24.1.?, $\ldots$	$[(9, 24)]$	$1$
539.b1	539a1	539.b	539a	$3$	$9$	\( 7^{2} \cdot 11 \)	\( - 7^{8} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1386$	$144$	$3$	$1$	$1$		$0$	$320$	$0.677956$	$-78843215872/539$	$1.00604$	$5.84545$	$[0, -1, 1, -4377, -110013]$	\(y^2+y=x^3-x^2-4377x-110013\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 22.2.0.a.1, 63.72.0-63.e.1.3, $\ldots$	$[ ]$	$1$
539.b2	539a2	539.b	539a	$3$	$9$	\( 7^{2} \cdot 11 \)	\( - 7^{12} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1386$	$144$	$3$	$1$	$1$		$0$	$960$	$1.227262$	$-13278380032/156590819$	$1.06522$	$6.04912$	$[0, -1, 1, -2417, -210708]$	\(y^2+y=x^3-x^2-2417x-210708\)	3.12.0.a.1, 21.24.0-3.a.1.1, 22.2.0.a.1, 63.72.0-63.b.1.2, 66.24.1.b.1, $\ldots$	$[ ]$	$1$
539.b3	539a3	539.b	539a	$3$	$9$	\( 7^{2} \cdot 11 \)	\( - 7^{8} \cdot 11^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1386$	$144$	$3$	$1$	$1$		$0$	$2880$	$1.776567$	$9463555063808/115539436859$	$1.06593$	$7.08371$	$[0, -1, 1, 21593, 5467657]$	\(y^2+y=x^3-x^2+21593x+5467657\)	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 22.2.0.a.1, 63.72.0-63.e.2.3, $\ldots$	$[ ]$	$1$
539.c1	539b1	539.c	539b	$1$	$1$	\( 7^{2} \cdot 11 \)	\( - 7^{8} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$192$	$0.186301$	$884736/539$	$1.02512$	$4.03333$	$[0, 0, 1, 98, -86]$	\(y^2+y=x^3+98x-86\)	22.2.0.a.1	$[ ]$	$1$
539.d1	539c2	539.d	539c	$2$	$2$	\( 7^{2} \cdot 11 \)	\( 7^{12} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.960603622$	$1$		$0$	$576$	$0.886935$	$15124197817/1294139$	$0.97750$	$5.58293$	$[1, 0, 1, -2525, -45279]$	\(y^2+xy+y=x^3-2525x-45279\)	2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.?	$[(-117/2, 603/2)]$	$1$
539.d2	539c1	539.d	539c	$2$	$2$	\( 7^{2} \cdot 11 \)	\( - 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$1.480301811$	$1$		$3$	$288$	$0.540362$	$4657463/41503$	$0.89262$	$4.72145$	$[1, 0, 1, 170, -3237]$	\(y^2+xy+y=x^3+170x-3237\)	2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.?	$[(123, 1310)]$	$1$

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