Elliptic curves over $\Q$ of conductor 37479

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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
37479.a1	37479e1	37479.a	37479e	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( - 3^{10} \cdot 13 \cdot 31^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$806$	$2$	$0$	$1.130227120$	$1$		$4$	$1382400$	$2.392925$	$-9571339399168/22868673867$	$0.95470$	$4.94976$	$[0, 1, 1, -425082, 241438214]$	\(y^2+y=x^3+x^2-425082x+241438214\)	806.2.0.?	$[(537, 12973)]$	$1$
37479.b1	37479a1	37479.b	37479a	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( - 3^{4} \cdot 13 \cdot 31^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$806$	$2$	$0$	$1$	$1$		$0$	$61440$	$1.317490$	$-262144000/32643$	$0.90123$	$3.81551$	$[0, -1, 1, -12813, -611134]$	\(y^2+y=x^3-x^2-12813x-611134\)	806.2.0.?	$[ ]$	$1$
37479.c1	37479c1	37479.c	37479c	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( 3 \cdot 13^{5} \cdot 31^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$156$	$2$	$0$	$1$	$1$		$0$	$18000$	$0.437002$	$3580540393/1113879$	$0.89452$	$2.74098$	$[1, 1, 0, -314, 1329]$	\(y^2+xy=x^3+x^2-314x+1329\)	156.2.0.?	$[ ]$	$1$
37479.d1	37479b1	37479.d	37479b	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( - 3^{2} \cdot 13 \cdot 31^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$424080$	$2.087532$	$-15015625/117$	$0.93598$	$4.83100$	$[1, 1, 0, -481000, -129462359]$	\(y^2+xy=x^3+x^2-481000x-129462359\)	52.2.0.a.1	$[ ]$	$1$
37479.e1	37479g1	37479.e	37479g	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( 3 \cdot 13^{5} \cdot 31^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$156$	$2$	$0$	$1.900255422$	$1$		$0$	$558000$	$2.153996$	$3580540393/1113879$	$0.89452$	$4.69738$	$[1, 0, 1, -302255, -43519393]$	\(y^2+xy+y=x^3-302255x-43519393\)	156.2.0.?	$[(-4085/3, 18607/3)]$	$1$
37479.f1	37479f1	37479.f	37479f	$1$	$1$	\( 3 \cdot 13 \cdot 31^{2} \)	\( - 3^{2} \cdot 13 \cdot 31^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.561322603$	$1$		$2$	$13680$	$0.370539$	$-15015625/117$	$0.93598$	$2.87460$	$[1, 0, 1, -501, 4297]$	\(y^2+xy+y=x^3-501x+4297\)	52.2.0.a.1	$[(-13, 99)]$	$1$
37479.g1	37479d4	37479.g	37479d	$4$	$4$	\( 3 \cdot 13 \cdot 31^{2} \)	\( 3^{4} \cdot 13 \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9672$	$48$	$0$	$4.371475191$	$1$		$2$	$120960$	$1.398626$	$37159393753/1053$	$1.11616$	$4.26741$	$[1, 0, 1, -66810, 6640963]$	\(y^2+xy+y=x^3-66810x+6640963\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[(23, 2250)]$	$1$
37479.g2	37479d3	37479.g	37479d	$4$	$4$	\( 3 \cdot 13 \cdot 31^{2} \)	\( 3 \cdot 13^{4} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9672$	$48$	$0$	$17.48590076$	$1$		$0$	$120960$	$1.398626$	$822656953/85683$	$0.96086$	$3.90560$	$[1, 0, 1, -18760, -897121]$	\(y^2+xy+y=x^3-18760x-897121\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 104.12.0.?, 124.12.0.?, $\ldots$	$[(-25494621/650, 42954317567/650)]$	$1$
37479.g3	37479d2	37479.g	37479d	$4$	$4$	\( 3 \cdot 13 \cdot 31^{2} \)	\( 3^{2} \cdot 13^{2} \cdot 31^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4836$	$48$	$0$	$8.742950383$	$1$		$2$	$60480$	$1.052053$	$10218313/1521$	$0.91403$	$3.48891$	$[1, 0, 1, -4345, 94631]$	\(y^2+xy+y=x^3-4345x+94631\)	2.6.0.a.1, 12.12.0.a.1, 52.12.0.b.1, 124.12.0.?, 156.24.0.?, $\ldots$	$[(781/13, 594125/13)]$	$1$
37479.g4	37479d1	37479.g	37479d	$4$	$4$	\( 3 \cdot 13 \cdot 31^{2} \)	\( - 3 \cdot 13 \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9672$	$48$	$0$	$17.48590076$	$1$		$1$	$30240$	$0.705480$	$12167/39$	$0.85844$	$2.99321$	$[1, 0, 1, 460, 8141]$	\(y^2+xy+y=x^3+460x+8141\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 78.6.0.?, 104.12.0.?, $\ldots$	$[(23180083/897, 143237917438/897)]$	$1$

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