Elliptic curves over $\Q$ of conductor 160113

Results (14 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
160113.a1	160113a1	160113.a	160113a	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{2} \cdot 19 \cdot 53^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1.125863816$	$1$		$2$	$1648512$	$1.763296$	$217088/171$	$0.68811$	$3.67588$	$[0, 1, 1, 49626, 2573642]$	\(y^2+y=x^3+x^2+49626x+2573642\)	38.2.0.a.1	$[(936, 29494)]$
160113.b1	160113b1	160113.b	160113b	$2$	$2$	\( 3 \cdot 19 \cdot 53^{2} \)	\( 3^{5} \cdot 19 \cdot 53^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12084$	$12$	$0$	$1$	$1$		$1$	$2021760$	$2.060905$	$53540005609/12969153$	$0.99776$	$4.04931$	$[1, 1, 1, -220565, -30493654]$	\(y^2+xy+y=x^3+x^2-220565x-30493654\)	2.3.0.a.1, 114.6.0.?, 212.6.0.?, 12084.12.0.?	$[]$
160113.b2	160113b2	160113.b	160113b	$2$	$2$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{10} \cdot 19^{2} \cdot 53^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12084$	$12$	$0$	$1$	$1$		$0$	$4043520$	$2.407478$	$717157709351/1129784517$	$0.89198$	$4.31121$	$[1, 1, 1, 523820, -191280814]$	\(y^2+xy+y=x^3+x^2+523820x-191280814\)	2.3.0.a.1, 212.6.0.?, 228.6.0.?, 12084.12.0.?	$[]$
160113.c1	160113c1	160113.c	160113c	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{14} \cdot 19 \cdot 53^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$4$	$2$	$0$	$843696$	$1.636427$	$-1178642372740721641/90876411$	$0.98935$	$4.13493$	$[1, 1, 1, -310506, -66726150]$	\(y^2+xy+y=x^3+x^2-310506x-66726150\)	38.2.0.a.1	$[]$
160113.d1	160113d3	160113.d	160113d	$4$	$4$	\( 3 \cdot 19 \cdot 53^{2} \)	\( 3^{4} \cdot 19 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$0$	$898560$	$1.740137$	$115714886617/1539$	$0.98111$	$4.11362$	$[1, 1, 1, -285172, 58495466]$	\(y^2+xy+y=x^3+x^2-285172x+58495466\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 76.12.0.?, 212.12.0.?, $\ldots$	$[]$
160113.d2	160113d2	160113.d	160113d	$4$	$4$	\( 3 \cdot 19 \cdot 53^{2} \)	\( 3^{2} \cdot 19^{2} \cdot 53^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12084$	$48$	$0$	$1$	$1$		$2$	$449280$	$1.393564$	$30664297/3249$	$0.90727$	$3.42637$	$[1, 1, 1, -18317, 854786]$	\(y^2+xy+y=x^3+x^2-18317x+854786\)	2.6.0.a.1, 12.12.0.b.1, 76.12.0.?, 212.12.0.?, 228.24.0.?, $\ldots$	$[]$
160113.d3	160113d1	160113.d	160113d	$4$	$4$	\( 3 \cdot 19 \cdot 53^{2} \)	\( 3 \cdot 19 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$1$	$224640$	$1.046989$	$389017/57$	$0.96267$	$3.06194$	$[1, 1, 1, -4272, -94656]$	\(y^2+xy+y=x^3+x^2-4272x-94656\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 114.6.0.?, 152.12.0.?, $\ldots$	$[]$
160113.d4	160113d4	160113.d	160113d	$4$	$4$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3 \cdot 19^{4} \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$24168$	$48$	$0$	$1$	$1$		$0$	$898560$	$1.740137$	$67419143/390963$	$0.97474$	$3.67565$	$[1, 1, 1, 23818, 4259294]$	\(y^2+xy+y=x^3+x^2+23818x+4259294\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 152.12.0.?, $\ldots$	$[]$
160113.e1	160113e1	160113.e	160113e	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{14} \cdot 19 \cdot 53^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$15.58255622$	$1$		$0$	$44715888$	$3.621574$	$-1178642372740721641/90876411$	$0.98935$	$6.12279$	$[1, 0, 1, -872211413, -9914800356025]$	\(y^2+xy+y=x^3-872211413x-9914800356025\)	38.2.0.a.1	$[(5927439621/319, 378888966880009/319)]$
160113.f1	160113g2	160113.f	160113g	$2$	$5$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{2} \cdot 19^{5} \cdot 53^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$10070$	$48$	$1$	$1$	$1$		$0$	$8985600$	$2.636555$	$-9358714467168256/22284891$	$1.06833$	$5.05663$	$[0, -1, 1, -12332446, -16665400125]$	\(y^2+y=x^3-x^2-12332446x-16665400125\)	5.12.0.a.2, 38.2.0.a.1, 190.24.1.?, 265.24.0.?, 10070.48.1.?	$[]$
160113.f2	160113g1	160113.f	160113g	$2$	$5$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{10} \cdot 19 \cdot 53^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$10070$	$48$	$1$	$1$	$1$		$0$	$1797120$	$1.831835$	$841232384/1121931$	$1.00490$	$3.72491$	$[0, -1, 1, 55244, -5726745]$	\(y^2+y=x^3-x^2+55244x-5726745\)	5.12.0.a.1, 38.2.0.a.1, 190.24.1.?, 265.24.0.?, 10070.48.1.?	$[]$
160113.g1	160113h1	160113.g	160113h	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{2} \cdot 19 \cdot 53^{14} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$25$	$5$	$0$	$113218560$	$3.916149$	$-2584989816536277323776/10646407060342731$	$1.00462$	$6.10273$	$[0, -1, 1, -803150216, 8792177363195]$	\(y^2+y=x^3-x^2-803150216x+8792177363195\)	38.2.0.a.1	$[]$
160113.h1	160113i1	160113.h	160113i	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{2} \cdot 19 \cdot 53^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$31104$	$-0.221849$	$217088/171$	$0.68811$	$1.68802$	$[0, -1, 1, 18, 11]$	\(y^2+y=x^3-x^2+18x+11\)	38.2.0.a.1	$[]$
160113.i1	160113f1	160113.i	160113f	$1$	$1$	\( 3 \cdot 19 \cdot 53^{2} \)	\( - 3^{2} \cdot 19 \cdot 53^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$6.585512574$	$1$		$0$	$585728$	$1.148598$	$-1404928/171$	$0.86512$	$3.18502$	$[0, 1, 1, -6554, 222509]$	\(y^2+y=x^3+x^2-6554x+222509\)	38.2.0.a.1	$[(30169/32, 7728029/32)]$