Elliptic curves over $\Q$ of conductor 2080

Results (16 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
2080.a1	2080d1	2080.a	2080d	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5 \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$520$	$48$	$0$	$1.194050064$	$1$		$13$	$384$	$-0.242941$	$1111934656/65$	$0.93766$	$3.27066$	$[0, 1, 0, -86, 280]$	\(y^2=x^3+x^2-86x+280\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.12.0.?, $\ldots$	$[(6, 4), (1, 14)]$
2080.a2	2080d2	2080.a	2080d	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{2} \cdot 13^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.37	2B	$520$	$48$	$0$	$0.298512516$	$1$		$29$	$768$	$0.103632$	$-14526784/4225$	$0.88671$	$3.30053$	$[0, 1, 0, -81, 319]$	\(y^2=x^3+x^2-81x+319\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.?	$[(-1, 20), (9, 20)]$
2080.b1	2080b1	2080.b	2080b	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$520$	$48$	$0$	$1$	$1$		$1$	$256$	$0.071611$	$140283769536/325$	$1.22475$	$3.90384$	$[0, 0, 0, -433, -3468]$	\(y^2=x^3-433x-3468\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 26.6.0.b.1, 52.12.0.e.1, $\ldots$	$[]$
2080.b2	2080b2	2080.b	2080b	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.37	2B	$520$	$48$	$0$	$1$	$1$		$1$	$512$	$0.418184$	$-2116874304/105625$	$0.98956$	$3.91010$	$[0, 0, 0, -428, -3552]$	\(y^2=x^3-428x-3552\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$	$[]$
2080.c1	2080a1	2080.c	2080a	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$520$	$48$	$0$	$0.896014826$	$1$		$7$	$256$	$0.071611$	$140283769536/325$	$1.22475$	$3.90384$	$[0, 0, 0, -433, 3468]$	\(y^2=x^3-433x+3468\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 26.6.0.b.1, 52.12.0.e.1, $\ldots$	$[(11, 6)]$
2080.c2	2080a2	2080.c	2080a	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.37	2B	$520$	$48$	$0$	$0.448007413$	$1$		$9$	$512$	$0.418184$	$-2116874304/105625$	$0.98956$	$3.91010$	$[0, 0, 0, -428, 3552]$	\(y^2=x^3-428x+3552\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$	$[(2, 52)]$
2080.d1	2080f2	2080.d	2080f	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{9} \cdot 5^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.57	2B	$1040$	$192$	$3$	$1$	$4$	$2$	$1$	$1024$	$0.496668$	$9001508089608/325$	$0.99017$	$4.72070$	$[0, 0, 0, -3467, -78574]$	\(y^2=x^3-3467x-78574\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 80.48.0.?, 104.48.0.?, $\ldots$	$[]$
2080.d2	2080f3	2080.d	2080f	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{9} \cdot 5^{8} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.47	2B	$1040$	$192$	$3$	$1$	$1$		$3$	$1024$	$0.496668$	$9024895368/5078125$	$1.17370$	$3.81690$	$[0, 0, 0, -347, 414]$	\(y^2=x^3-347x+414\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 80.48.0.?, 104.48.0.?, $\ldots$	$[]$
2080.d3	2080f1	2080.d	2080f	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.7	2Cs	$1040$	$192$	$3$	$1$	$1$		$3$	$512$	$0.150095$	$17657244864/105625$	$1.13826$	$3.63257$	$[0, 0, 0, -217, -1224]$	\(y^2=x^3-217x-1224\)	2.6.0.a.1, 4.24.0-4.a.1.1, 40.48.0-40.j.1.1, 104.48.0.?, 208.96.0.?, $\ldots$	$[]$
2080.d4	2080f4	2080.d	2080f	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{2} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.11	2B	$1040$	$192$	$3$	$1$	$1$		$3$	$1024$	$0.496668$	$-21024576/714025$	$1.05309$	$3.83084$	$[0, 0, 0, -92, -2624]$	\(y^2=x^3-92x-2624\)	2.3.0.a.1, 4.24.0-4.d.1.1, 40.48.0-40.z.1.3, 104.48.0.?, 208.96.0.?, $\ldots$	$[]$
2080.e1	2080e3	2080.e	2080e	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{9} \cdot 5^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.47	2B	$1040$	$192$	$3$	$1$	$4$	$2$	$3$	$1024$	$0.496668$	$9001508089608/325$	$0.99017$	$4.72070$	$[0, 0, 0, -3467, 78574]$	\(y^2=x^3-3467x+78574\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 80.48.0.?, 104.48.0.?, $\ldots$	$[]$
2080.e2	2080e2	2080.e	2080e	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{9} \cdot 5^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.57	2B	$1040$	$192$	$3$	$1$	$1$		$1$	$1024$	$0.496668$	$9024895368/5078125$	$1.17370$	$3.81690$	$[0, 0, 0, -347, -414]$	\(y^2=x^3-347x-414\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 80.48.0.?, 104.48.0.?, $\ldots$	$[]$
2080.e3	2080e1	2080.e	2080e	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.7	2Cs	$1040$	$192$	$3$	$1$	$1$		$3$	$512$	$0.150095$	$17657244864/105625$	$1.13826$	$3.63257$	$[0, 0, 0, -217, 1224]$	\(y^2=x^3-217x+1224\)	2.6.0.a.1, 4.24.0-4.a.1.1, 40.48.0-40.j.1.1, 104.48.0.?, 208.96.0.?, $\ldots$	$[]$
2080.e4	2080e4	2080.e	2080e	$4$	$4$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{2} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.11	2B	$1040$	$192$	$3$	$1$	$1$		$3$	$1024$	$0.496668$	$-21024576/714025$	$1.05309$	$3.83084$	$[0, 0, 0, -92, 2624]$	\(y^2=x^3-92x+2624\)	2.3.0.a.1, 4.24.0-4.d.1.1, 40.48.0-40.z.1.3, 104.48.0.?, 208.96.0.?, $\ldots$	$[]$
2080.f1	2080c1	2080.f	2080c	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 5 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$520$	$48$	$0$	$1$	$4$	$2$	$1$	$384$	$-0.242941$	$1111934656/65$	$0.93766$	$3.27066$	$[0, -1, 0, -86, -280]$	\(y^2=x^3-x^2-86x-280\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 130.6.0.?, 260.12.0.?, $\ldots$	$[]$
2080.f2	2080c2	2080.f	2080c	$2$	$2$	\( 2^{5} \cdot 5 \cdot 13 \)	\( - 2^{12} \cdot 5^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.37	2B	$520$	$48$	$0$	$1$	$1$		$1$	$768$	$0.103632$	$-14526784/4225$	$0.88671$	$3.30053$	$[0, -1, 0, -81, -319]$	\(y^2=x^3-x^2-81x-319\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.48.0.?	$[]$