Elliptic curves over $\Q$ of conductor 31117

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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
31117.a1	31117c1	31117.a	31117c	$1$	$1$	\( 29^{2} \cdot 37 \)	\( - 29^{9} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4292$	$2$	$0$	$1$	$1$		$0$	$161280$	$1.512289$	$-253636137/902393$	$0.83883$	$4.01353$	$[1, -1, 1, -11091, -1199148]$	\(y^2+xy+y=x^3-x^2-11091x-1199148\)	4292.2.0.?	$[ ]$
31117.b1	31117f1	31117.b	31117f	$1$	$1$	\( 29^{2} \cdot 37 \)	\( - 29^{3} \cdot 37^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$0.413813147$	$1$		$12$	$30688$	$0.830666$	$-6616084455917/1369$	$0.93164$	$3.82991$	$[1, 1, 1, -11342, 460200]$	\(y^2+xy+y=x^3+x^2-11342x+460200\)	116.2.0.?	$[(60, -45), (247/2, -177/2)]$
31117.c1	31117h1	31117.c	31117h	$1$	$1$	\( 29^{2} \cdot 37 \)	\( - 29^{3} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4292$	$2$	$0$	$1.701822499$	$1$		$0$	$2240$	$-0.178070$	$-125/37$	$0.77779$	$2.04625$	$[1, 0, 0, -3, -46]$	\(y^2+xy=x^3-3x-46\)	4292.2.0.?	$[(19/2, 39/2)]$
31117.d1	31117a3	31117.d	31117a	$3$	$9$	\( 29^{2} \cdot 37 \)	\( 29^{6} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$57942$	$1296$	$43$	$6.938596966$	$1$		$2$	$145152$	$1.905729$	$727057727488000/37$	$1.08598$	$5.26062$	$[0, -1, 1, -1575473, -760615110]$	\(y^2+y=x^3-x^2-1575473x-760615110\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 87.8.0.?, $\ldots$	$[(29184, 4980822)]$
31117.d2	31117a2	31117.d	31117a	$3$	$9$	\( 29^{2} \cdot 37 \)	\( 29^{6} \cdot 37^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$57942$	$1296$	$43$	$2.312865655$	$1$		$2$	$48384$	$1.356422$	$1404928000/50653$	$0.97274$	$3.98888$	$[0, -1, 1, -19623, -1018023]$	\(y^2+y=x^3-x^2-19623x-1018023\)	3.12.0.a.1, 9.36.0.b.1, 74.2.0.?, 87.24.0.?, 222.24.1.?, $\ldots$	$[(213, 2102)]$
31117.d3	31117a1	31117.d	31117a	$3$	$9$	\( 29^{2} \cdot 37 \)	\( 29^{6} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$57942$	$1296$	$43$	$0.770955218$	$1$		$4$	$16128$	$0.807117$	$4096000/37$	$0.88268$	$3.42461$	$[0, -1, 1, -2803, 57616]$	\(y^2+y=x^3-x^2-2803x+57616\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 87.8.0.?, $\ldots$	$[(68, 420)]$
31117.e1	31117b1	31117.e	31117b	$1$	$1$	\( 29^{2} \cdot 37 \)	\( 29^{8} \cdot 37 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$74$	$2$	$0$	$4.541742074$	$1$		$6$	$107520$	$1.414724$	$10303307776/31117$	$0.89776$	$4.18148$	$[0, 1, 1, -38125, 2845095]$	\(y^2+y=x^3+x^2-38125x+2845095\)	74.2.0.?	$[(135, 420), (-467/3, 58436/3)]$
31117.f1	31117e1	31117.f	31117e	$1$	$1$	\( 29^{2} \cdot 37 \)	\( - 29^{9} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4292$	$2$	$0$	$1$	$1$		$0$	$64960$	$1.505577$	$-125/37$	$0.77779$	$3.99915$	$[1, 1, 0, -2540, -1116827]$	\(y^2+xy=x^3+x^2-2540x-1116827\)	4292.2.0.?	$[ ]$
31117.g1	31117g1	31117.g	31117g	$1$	$1$	\( 29^{2} \cdot 37 \)	\( - 29^{9} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$2.770953067$	$1$		$0$	$889952$	$2.514313$	$-6616084455917/1369$	$0.93164$	$5.78282$	$[1, 0, 1, -9538640, 11338285807]$	\(y^2+xy+y=x^3-9538640x+11338285807\)	116.2.0.?	$[(44641/5, -87276/5)]$
31117.h1	31117d1	31117.h	31117d	$1$	$1$	\( 29^{2} \cdot 37 \)	\( 29^{6} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$74$	$2$	$0$	$1$	$4$	$2$	$0$	$48384$	$0.687106$	$110592/37$	$0.76978$	$3.07548$	$[0, 0, 1, -841, 6097]$	\(y^2+y=x^3-841x+6097\)	74.2.0.?	$[ ]$

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