Elliptic curves over $\Q$ of conductor 800

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
800.a1	800c1	800.a	800c	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$40$	$48$	$0$	$1.285907433$	$1$		$5$	$192$	$0.098674$	$438976/5$	$0.87813$	$4.01036$	$[0, 1, 0, -158, -812]$	\(y^2=x^3+x^2-158x-812\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 10.6.0.a.1, 20.12.0.e.1, $\ldots$	$[(-8, 2)]$
800.a2	800c2	800.a	800c	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{12} \cdot 5^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.38	2B	$40$	$48$	$0$	$0.642953716$	$1$		$9$	$384$	$0.445248$	$-64/25$	$1.09219$	$4.28588$	$[0, 1, 0, -33, -1937]$	\(y^2=x^3+x^2-33x-1937\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.2, 20.12.0.d.1, 40.48.0-40.t.1.4	$[(23, 100)]$
800.b1	800i1	800.b	800i	$1$	$1$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{9} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.1, 5.15.0.1	5Ns	$40$	$60$	$3$	$0.196377791$	$1$		$6$	$240$	$0.315584$	$-5000$	$0.99499$	$4.17793$	$[0, -1, 0, -208, 1412]$	\(y^2=x^3-x^2-208x+1412\)	5.15.0.a.1, 8.2.0.a.1, 20.30.0.b.1, 40.60.3.u.1	$[(-8, 50)]$
800.c1	800f1	800.c	800f	$1$	$1$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{9} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.1, 5.15.0.1	5Ns	$40$	$60$	$3$	$1$	$1$		$0$	$48$	$-0.489135$	$-5000$	$0.99499$	$2.73333$	$[0, -1, 0, -8, -8]$	\(y^2=x^3-x^2-8x-8\)	5.15.0.a.1, 8.2.0.a.1, 20.30.0.b.1, 40.60.3.u.1	$[]$
800.d1	800a2	800.d	800a	$4$	$4$	\( 2^{5} \cdot 5^{2} \)	\( 2^{9} \cdot 5^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$3.798964345$	$1$		$1$	$128$	$0.187333$	$287496$	$1.17246$	$4.25813$	$[0, 0, 0, -275, -1750]$	\(y^2=x^3-275x-1750\)		$[(-86/3, 62/3)]$
800.d2	800a3	800.d	800a	$4$	$4$	\( 2^{5} \cdot 5^{2} \)	\( 2^{9} \cdot 5^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$0.949741086$	$1$		$7$	$128$	$0.187333$	$287496$	$1.17246$	$4.25813$	$[0, 0, 0, -275, 1750]$	\(y^2=x^3-275x+1750\)		$[(9, 2)]$
800.d3	800a1	800.d	800a	$4$	$4$	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.143	2Cs				$1.899482172$	$1$		$7$	$64$	$-0.159240$	$1728$		$3.18197$	$[0, 0, 0, -25, 0]$	\(y^2=x^3-25x\)		$[(-4, 6)]$
800.d4	800a4	800.d	800a	$4$	$4$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{12} \cdot 5^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.178	2B				$0.949741086$	$1$		$5$	$128$	$0.187333$	$1728$		$3.80413$	$[0, 0, 0, 100, 0]$	\(y^2=x^3+100x\)		$[(5, 25)]$
800.e1	800h1	800.e	800h	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$0.635528714$	$1$		$5$	$32$	$-0.561600$	$1728$		$2.45967$	$[0, 0, 0, -5, 0]$	\(y^2=x^3-5x\)		$[(-1, 2)]$
800.e2	800h2	800.e	800h	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{12} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1.271057428$	$1$		$7$	$64$	$-0.215026$	$1728$		$3.08182$	$[0, 0, 0, 20, 0]$	\(y^2=x^3+20x\)		$[(4, 12)]$
800.f1	800d1	800.f	800d	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$160$	$0.243119$	$1728$		$3.90427$	$[0, 0, 0, -125, 0]$	\(y^2=x^3-125x\)		$[]$
800.f2	800d2	800.f	800d	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{12} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$320$	$0.589693$	$1728$		$4.52643$	$[0, 0, 0, 500, 0]$	\(y^2=x^3+500x\)		$[]$
800.g1	800b1	800.g	800b	$1$	$1$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{9} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.1, 5.15.0.1	5Ns	$40$	$60$	$3$	$0.318472330$	$1$		$4$	$48$	$-0.489135$	$-5000$	$0.99499$	$2.73333$	$[0, 1, 0, -8, 8]$	\(y^2=x^3+x^2-8x+8\)	5.15.0.a.1, 8.2.0.a.1, 20.30.0.b.1, 40.60.3.u.1	$[(2, 2)]$
800.h1	800e1	800.h	800e	$1$	$1$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{9} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.1, 5.15.0.1	5Ns	$40$	$60$	$3$	$1$	$1$		$0$	$240$	$0.315584$	$-5000$	$0.99499$	$4.17793$	$[0, 1, 0, -208, -1412]$	\(y^2=x^3+x^2-208x-1412\)	5.15.0.a.1, 8.2.0.a.1, 20.30.0.b.1, 40.60.3.u.1	$[]$
800.i1	800g1	800.i	800g	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$40$	$48$	$0$	$1$	$1$		$1$	$192$	$0.098674$	$438976/5$	$0.87813$	$4.01036$	$[0, -1, 0, -158, 812]$	\(y^2=x^3-x^2-158x+812\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 10.6.0.a.1, 20.12.0.e.1, $\ldots$	$[]$
800.i2	800g2	800.i	800g	$2$	$2$	\( 2^{5} \cdot 5^{2} \)	\( - 2^{12} \cdot 5^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.38	2B	$40$	$48$	$0$	$1$	$1$		$1$	$384$	$0.445248$	$-64/25$	$1.09219$	$4.28588$	$[0, -1, 0, -33, 1937]$	\(y^2=x^3-x^2-33x+1937\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.2, 20.12.0.d.1, 40.48.0-40.t.1.7	$[]$