Elliptic curves over Q\Q of conductor 164331

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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
164331.a1	164331a3	164331.a	164331a	$4$	$4$	$3^{2} \cdot 19 \cdot 31^{2}$	$3^{10} \cdot 19 \cdot 31^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$14136$	$48$	$0$	$2.250733793$	$1$		$4$	$1382400$	$2.021290$	$115714886617/1539$	$0.98111$	$4.38564$	$[1, -1, 1, -878054, 316902498]$	$y^2+xy+y=x^3-x^2-878054x+316902498$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 76.12.0.?, 248.12.0.?, $\ldots$	$[(536, -66)]$
164331.a2	164331a2	164331.a	164331a	$4$	$4$	$3^{2} \cdot 19 \cdot 31^{2}$	$3^{8} \cdot 19^{2} \cdot 31^{6}$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7068$	$48$	$0$	$4.501467586$	$1$		$4$	$691200$	$1.674717$	$30664297/3249$	$0.90727$	$3.69988$	$[1, -1, 1, -56399, 4673598]$	$y^2+xy+y=x^3-x^2-56399x+4673598$	2.6.0.a.1, 12.12.0.b.1, 76.12.0.?, 124.12.0.?, 228.24.0.?, $\ldots$	$[(-46, 2700)]$
164331.a3	164331a1	164331.a	164331a	$4$	$4$	$3^{2} \cdot 19 \cdot 31^{2}$	$3^{7} \cdot 19 \cdot 31^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$14136$	$48$	$0$	$9.002935172$	$1$		$1$	$345600$	$1.328144$	$389017/57$	$0.96267$	$3.33624$	$[1, -1, 1, -13154, -498504]$	$y^2+xy+y=x^3-x^2-13154x-498504$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 114.6.0.?, 124.12.0.?, $\ldots$	$[(-13540/17, 678531/17)]$
164331.a4	164331a4	164331.a	164331a	$4$	$4$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{7} \cdot 19^{4} \cdot 31^{6}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$14136$	$48$	$0$	$2.250733793$	$1$		$2$	$1382400$	$2.021290$	$67419143/390963$	$0.97474$	$3.94862$	$[1, -1, 1, 73336, 22940286]$	$y^2+xy+y=x^3-x^2+73336x+22940286$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 124.12.0.?, $\ldots$	$[(938, 29802)]$
164331.b1	164331b3	164331.b	164331b	$3$	$9$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{6} \cdot 19 \cdot 31^{6}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$31806$	$1296$	$43$	$1$	$9$	$3$	$0$	$2177280$	$2.299740$	$-50357871050752/19$	$1.10495$	$4.89155$	$[0, 0, 1, -6653964, -6606459608]$	$y^2+y=x^3-6653964x-6606459608$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 93.8.0.?, $\ldots$	$[]$
164331.b2	164331b2	164331.b	164331b	$3$	$9$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{6} \cdot 19^{3} \cdot 31^{6}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$31806$	$1296$	$43$	$1$	$1$		$0$	$725760$	$1.750433$	$-89915392/6859$	$1.03310$	$3.79976$	$[0, 0, 1, -80724, -9391613]$	$y^2+y=x^3-80724x-9391613$	3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 93.24.0.?, 114.24.1.?, $\ldots$	$[]$
164331.b3	164331b1	164331.b	164331b	$3$	$9$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{6} \cdot 19 \cdot 31^{6}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$31806$	$1296$	$43$	$1$	$1$		$0$	$241920$	$1.201126$	$32768/19$	$1.31757$	$3.13022$	$[0, 0, 1, 5766, -7448]$	$y^2+y=x^3+5766x-7448$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 93.8.0.?, $\ldots$	$[]$
164331.c1	164331c2	164331.c	164331c	$2$	$5$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{8} \cdot 19^{5} \cdot 31^{6}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$17670$	$48$	$1$	$131.1477325$	$1$		$0$	$14688000$	$2.917706$	$-9358714467168256/22284891$	$1.06833$	$5.32661$	$[0, 0, 1, -37971993, -90062520143]$	$y^2+y=x^3-37971993x-90062520143$	5.12.0.a.2, 38.2.0.a.1, 190.24.1.?, 465.24.0.?, 17670.48.1.?	$[(71140469028244895647204282191663973303453705751733971470081/1914606809503225329150695876, 17869072816297222539664034493850137844134815355299961188268697397450181683274629666864609/1914606809503225329150695876)]$
164331.c2	164331c1	164331.c	164331c	$2$	$5$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{16} \cdot 19 \cdot 31^{6}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$17670$	$48$	$1$	$26.22954651$	$1$		$0$	$2937600$	$2.112988$	$841232384/1121931$	$1.00490$	$3.99778$	$[0, 0, 1, 170097, -30841133]$	$y^2+y=x^3+170097x-30841133$	5.12.0.a.1, 38.2.0.a.1, 190.24.1.?, 465.24.0.?, 17670.48.1.?	$[(16399552003825/156892, 75103210144501426903/156892)]$
164331.d1	164331d1	164331.d	164331d	$1$	$1$	$3^{2} \cdot 19 \cdot 31^{2}$	$- 3^{8} \cdot 19 \cdot 31^{6}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$6.086362605$	$1$		$0$	$948480$	$1.429750$	$-1404928/171$	$0.86512$	$3.45905$	$[0, 0, 1, -20181, 1213983]$	$y^2+y=x^3-20181x+1213983$	38.2.0.a.1	$[(31961/20, 2668541/20)]$

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