Elliptic curves over $\Q$ of conductor 117

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

Results (4 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
117.a1	117a4	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{10} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$0.282583906$	$1$		$10$	$32$	$0.230940$	$37159393753/1053$	$1.11616$	$6.49497$	$2$	$[1, -1, 1, -626, 6180]$	\(y^2+xy+y=x^3-x^2-626x+6180\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[(8, 36)]$	$1$
117.a2	117a3	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{7} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$0.282583906$	$1$		$10$	$32$	$0.230940$	$822656953/85683$	$0.96086$	$5.69482$	$2$	$[1, -1, 1, -176, -768]$	\(y^2+xy+y=x^3-x^2-176x-768\)	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 104.24.0.?, 312.48.0.?	$[(-6, 9)]$	$1$
117.a3	117a2	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( 3^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$0.565167813$	$1$		$12$	$16$	$-0.115634$	$10218313/1521$	$0.91403$	$4.77332$	$1$	$[1, -1, 1, -41, 96]$	\(y^2+xy+y=x^3-x^2-41x+96\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 52.24.0-52.b.1.3, 156.48.0.?	$[(6, 3)]$	$1$
117.a4	117a1	117.a	117a	$4$	$4$	\( 3^{2} \cdot 13 \)	\( - 3^{7} \cdot 13 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$1.130335626$	$1$		$11$	$8$	$-0.462207$	$12167/39$	$0.85844$	$3.67707$	$1$	$[1, -1, 1, 4, 6]$	\(y^2+xy+y=x^3-x^2+4x+6\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 78.6.0.?, 104.24.0.?, $\ldots$	$[(0, 2)]$	$1$

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