Elliptic curves over $\Q$ of conductor 552

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

Results (14 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
552.a1	552a2	552.a	552a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{11} \cdot 3^{3} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$552$	$12$	$0$	$4.161950591$	$1$		$3$	$192$	$0.437473$	$80919167474/14283$	$0.96612$	$5.18589$	$1$	$[0, -1, 0, -1144, -14516]$	\(y^2=x^3-x^2-1144x-14516\)	2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.?	$[(45, 152)]$	$1$
552.a2	552a1	552.a	552a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( - 2^{10} \cdot 3^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$552$	$12$	$0$	$2.080975295$	$1$		$5$	$96$	$0.090899$	$-28756228/16767$	$0.89435$	$3.92850$	$1$	$[0, -1, 0, -64, -260]$	\(y^2=x^3-x^2-64x-260\)	2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.?	$[(18, 64)]$	$1$
552.b1	552b2	552.b	552b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{10} \cdot 3^{7} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$896$	$1.169321$	$10963069081334500/1156923$	$1.02886$	$6.94772$	$1$	$[0, -1, 0, -46648, 3893500]$	\(y^2=x^3-x^2-46648x+3893500\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[ ]$	$1$
552.b2	552b1	552.b	552b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( - 2^{8} \cdot 3^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$448$	$0.822747$	$-10627137250000/110008287$	$1.04721$	$5.63191$	$1$	$[0, -1, 0, -2908, 61876]$	\(y^2=x^3-x^2-2908x+61876\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[ ]$	$1$
552.c1	552d3	552.c	552d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{10} \cdot 3^{3} \cdot 23^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$552$	$48$	$0$	$2.871500307$	$1$		$5$	$384$	$0.619071$	$45989074372/7555707$	$0.96263$	$4.98660$	$1$	$[0, -1, 0, -752, 6972]$	\(y^2=x^3-x^2-752x+6972\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 184.24.0.?, 552.48.0.?	$[(46, 260)]$	$1$
552.c2	552d2	552.c	552d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{8} \cdot 3^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$276$	$48$	$0$	$1.435750153$	$1$		$11$	$192$	$0.272498$	$4135597648/385641$	$1.11158$	$4.38550$	$1$	$[0, -1, 0, -212, -1020]$	\(y^2=x^3-x^2-212x-1020\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 92.24.0.?, 276.48.0.?	$[(-8, 10)]$	$1$
552.c3	552d1	552.c	552d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{4} \cdot 3^{3} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$552$	$48$	$0$	$2.871500307$	$1$		$3$	$96$	$-0.074076$	$61604313088/621$	$1.06623$	$4.37418$	$2$	$[0, -1, 0, -207, -1080]$	\(y^2=x^3-x^2-207x-1080\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[(17, 5)]$	$1$
552.c4	552d4	552.c	552d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( - 2^{10} \cdot 3^{12} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$552$	$48$	$0$	$2.871500307$	$1$		$3$	$384$	$0.619071$	$1640689628/12223143$	$0.98661$	$4.85055$	$2$	$[0, -1, 0, 248, -5252]$	\(y^2=x^3-x^2+248x-5252\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 46.6.0.a.1, 92.24.0.?, $\ldots$	$[(38, 240)]$	$1$
552.d1	552c2	552.d	552c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{10} \cdot 3 \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$128$	$-0.065774$	$19307236/1587$	$1.01848$	$3.75501$	$1$	$[0, -1, 0, -56, -132]$	\(y^2=x^3-x^2-56x-132\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[ ]$	$1$
552.d2	552c1	552.d	552c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 23 \)	\( - 2^{8} \cdot 3^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$64$	$-0.412348$	$21296/207$	$0.81409$	$2.89397$	$1$	$[0, -1, 0, 4, -12]$	\(y^2=x^3-x^2+4x-12\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[ ]$	$1$
552.e1	552e4	552.e	552e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{11} \cdot 3 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$552$	$48$	$0$	$3.308313560$	$1$		$1$	$256$	$0.462658$	$1378334691074/69$	$1.07977$	$5.63495$	$2$	$[0, 1, 0, -2944, 60512]$	\(y^2=x^3+x^2-2944x+60512\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.y.1.6, 92.12.0.?, $\ldots$	$[(133/2, 177/2)]$	$1$
552.e2	552e3	552.e	552e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{11} \cdot 3 \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$552$	$48$	$0$	$3.308313560$	$1$		$3$	$256$	$0.462658$	$1522096994/839523$	$1.08605$	$4.55655$	$2$	$[0, 1, 0, -304, -544]$	\(y^2=x^3+x^2-304x-544\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.s.1.1, 184.24.0.?, 552.48.0.?	$[(19, 30)]$	$1$
552.e3	552e2	552.e	552e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( 2^{10} \cdot 3^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$552$	$48$	$0$	$1.654156780$	$1$		$7$	$128$	$0.116085$	$676449508/4761$	$0.99194$	$4.31831$	$1$	$[0, 1, 0, -184, 896]$	\(y^2=x^3+x^2-184x+896\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.b.1.4, 92.24.0.?, 552.48.0.?	$[(11, 18)]$	$1$
552.e4	552e1	552.e	552e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 23 \)	\( - 2^{8} \cdot 3^{4} \cdot 23 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$552$	$48$	$0$	$0.827078390$	$1$		$13$	$64$	$-0.230489$	$-35152/1863$	$0.89850$	$3.25343$	$1$	$[0, 1, 0, -4, 32]$	\(y^2=x^3+x^2-4x+32\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.y.1.4, 46.6.0.a.1, 92.24.0.?, $\ldots$	$[(-2, 6)]$	$1$

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