Elliptic curves over $\Q$ of conductor 171

Results (10 matches)

 

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
171.a1	171a3	171.a	171a	$4$	$4$	\( 3^{2} \cdot 19 \)	\( 3^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$456$	$48$	$0$	$1$	$1$		$0$	$48$	$0.304297$	$115714886617/1539$	$0.98111$	$6.23652$	$[1, -1, 1, -914, -10402]$	\(y^2+xy+y=x^3-x^2-914x-10402\)	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.z.1.4, $\ldots$	$[]$
171.a2	171a2	171.a	171a	$4$	$4$	\( 3^{2} \cdot 19 \)	\( 3^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$228$	$48$	$0$	$1$	$1$		$2$	$24$	$-0.042276$	$30664297/3249$	$0.90727$	$4.63474$	$[1, -1, 1, -59, -142]$	\(y^2+xy+y=x^3-x^2-59x-142\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 76.24.0.?, 228.48.0.?	$[]$
171.a3	171a1	171.a	171a	$4$	$4$	\( 3^{2} \cdot 19 \)	\( 3^{7} \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$456$	$48$	$0$	$1$	$1$		$3$	$12$	$-0.388850$	$389017/57$	$0.96267$	$3.78536$	$[1, -1, 1, -14, 20]$	\(y^2+xy+y=x^3-x^2-14x+20\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 114.6.0.?, 152.24.0.?, $\ldots$	$[]$
171.a4	171a4	171.a	171a	$4$	$4$	\( 3^{2} \cdot 19 \)	\( - 3^{7} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$456$	$48$	$0$	$1$	$1$		$0$	$48$	$0.304297$	$67419143/390963$	$0.97474$	$5.21575$	$[1, -1, 1, 76, -790]$	\(y^2+xy+y=x^3-x^2+76x-790\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 152.24.0.?, $\ldots$	$[]$
171.b1	171b3	171.b	171b	$3$	$9$	\( 3^{2} \cdot 19 \)	\( - 3^{6} \cdot 19 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	27.72.0.1	3B.1.1	$1026$	$1296$	$43$	$2.033701819$	$1$		$4$	$72$	$0.582746$	$-50357871050752/19$	$1.10495$	$7.41819$	$[0, 0, 1, -6924, 221760]$	\(y^2+y=x^3-6924x+221760\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$	$[(62, 175)]$
171.b2	171b2	171.b	171b	$3$	$9$	\( 3^{2} \cdot 19 \)	\( - 3^{6} \cdot 19^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.3	3Cs.1.1	$1026$	$1296$	$43$	$0.677900606$	$1$		$8$	$24$	$0.033439$	$-89915392/6859$	$1.03310$	$4.86805$	$[0, 0, 1, -84, 315]$	\(y^2+y=x^3-84x+315\)	3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$	$[(5, 4)]$
171.b3	171b1	171.b	171b	$3$	$9$	\( 3^{2} \cdot 19 \)	\( - 3^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.72.0.2	3B.1.2	$1026$	$1296$	$43$	$0.225966868$	$1$		$6$	$8$	$-0.515867$	$32768/19$	$1.31757$	$3.30416$	$[0, 0, 1, 6, 0]$	\(y^2+y=x^3+6x\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 38.2.0.a.1, 114.16.0.?, $\ldots$	$[(2, 4)]$
171.c1	171c2	171.c	171c	$2$	$5$	\( 3^{2} \cdot 19 \)	\( - 3^{8} \cdot 19^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$570$	$48$	$1$	$1$	$1$		$0$	$480$	$1.200714$	$-9358714467168256/22284891$	$1.06833$	$8.43438$	$[0, 0, 1, -39513, 3023145]$	\(y^2+y=x^3-39513x+3023145\)	5.12.0.a.2, 15.24.0-5.a.2.1, 38.2.0.a.1, 190.24.1.?, 570.48.1.?	$[]$
171.c2	171c1	171.c	171c	$2$	$5$	\( 3^{2} \cdot 19 \)	\( - 3^{16} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$570$	$48$	$1$	$1$	$1$		$0$	$96$	$0.395995$	$841232384/1121931$	$1.00490$	$5.33056$	$[0, 0, 1, 177, 1035]$	\(y^2+y=x^3+177x+1035\)	5.12.0.a.1, 15.24.0-5.a.1.1, 38.2.0.a.1, 190.24.1.?, 570.48.1.?	$[]$
171.d1	171d1	171.d	171d	$1$	$1$	\( 3^{2} \cdot 19 \)	\( - 3^{8} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$32$	$-0.287242$	$-1404928/171$	$0.86512$	$4.07223$	$[0, 0, 1, -21, -41]$	\(y^2+y=x^3-21x-41\)	38.2.0.a.1	$[]$