Elliptic curves over $\Q$ of conductor 200

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
200.a1	200a1	200.a	200a	$1$	$1$	\( 2^{3} \cdot 5^{2} \)	\( - 2^{11} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$120$	$0.391199$	$270$	$1.01898$	$5.24411$	$[0, 0, 0, 125, -1250]$	\(y^2=x^3+125x-1250\)	8.2.0.a.1	$[]$
200.b1	200b2	200.b	200b	$2$	$2$	\( 2^{3} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	16.96.3.346	2B	$80$	$384$	$9$	$0.146605513$	$1$		$13$	$16$	$-0.326646$	$78608$	$0.87912$	$4.08540$	$[0, 1, 0, -28, 48]$	\(y^2=x^3+x^2-28x+48\)	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 10.6.0.a.1, 16.96.3.ey.1, $\ldots$	$[(2, 2)]$
200.b2	200b1	200.b	200b	$2$	$2$	\( 2^{3} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	16.96.3.338	2B	$80$	$384$	$9$	$0.293211026$	$1$		$9$	$8$	$-0.673220$	$2048$	$1.01898$	$2.87365$	$[0, 1, 0, -3, -2]$	\(y^2=x^3+x^2-3x-2\)	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.1, 10.6.0.a.1, 16.96.3.ey.2, $\ldots$	$[(3, 5)]$
200.c1	200c3	200.c	200c	$4$	$4$	\( 2^{3} \cdot 5^{2} \)	\( 2^{10} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.57	2B	$80$	$192$	$3$	$1$	$1$		$1$	$96$	$0.602505$	$132304644/5$	$1.13632$	$6.66036$	$[0, 0, 0, -2675, -53250]$	\(y^2=x^3-2675x-53250\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.6, 10.6.0.a.1, 16.48.0-16.i.1.6, $\ldots$	$[]$
200.c2	200c2	200.c	200c	$4$	$4$	\( 2^{3} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.22	2Cs	$40$	$192$	$3$	$1$	$1$		$3$	$48$	$0.255931$	$148176/25$	$1.09175$	$5.11633$	$[0, 0, 0, -175, -750]$	\(y^2=x^3-175x-750\)	2.6.0.a.1, 4.24.0-4.a.1.2, 8.48.0-8.g.1.4, 20.48.0-20.b.1.2, 40.192.3-40.bk.1.4	$[]$
200.c3	200c1	200.c	200c	$4$	$4$	\( 2^{3} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.41	2B	$80$	$192$	$3$	$1$	$1$		$3$	$24$	$-0.090642$	$55296/5$	$1.01898$	$4.40700$	$[0, 0, 0, -50, 125]$	\(y^2=x^3-50x+125\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.8, 10.6.0.a.1, 16.48.0-16.i.1.8, $\ldots$	$[]$
200.c4	200c4	200.c	200c	$4$	$4$	\( 2^{3} \cdot 5^{2} \)	\( - 2^{10} \cdot 5^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.5	2B	$80$	$192$	$3$	$1$	$1$		$1$	$96$	$0.602505$	$237276/625$	$1.04671$	$5.70606$	$[0, 0, 0, 325, -4250]$	\(y^2=x^3+325x-4250\)	2.3.0.a.1, 4.24.0.c.1, 8.48.0-4.c.1.2, 20.48.0-4.c.1.1, 40.96.1-40.dk.1.2, $\ldots$	$[]$
200.d1	200d2	200.d	200d	$2$	$2$	\( 2^{3} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	16.96.3.346	2B	$80$	$384$	$9$	$1$	$1$		$1$	$80$	$0.478073$	$78608$	$0.87912$	$5.90798$	$[0, -1, 0, -708, 7412]$	\(y^2=x^3-x^2-708x+7412\)	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 10.6.0.a.1, 16.96.3.ey.1, $\ldots$	$[]$
200.d2	200d1	200.d	200d	$2$	$2$	\( 2^{3} \cdot 5^{2} \)	\( 2^{4} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	16.96.3.338	2B	$80$	$384$	$9$	$1$	$1$		$1$	$40$	$0.131500$	$2048$	$1.01898$	$4.69624$	$[0, -1, 0, -83, -88]$	\(y^2=x^3-x^2-83x-88\)	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.1, 10.6.0.a.1, 16.96.3.ey.2, $\ldots$	$[]$
200.e1	200e1	200.e	200e	$1$	$1$	\( 2^{3} \cdot 5^{2} \)	\( - 2^{11} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$24$	$-0.413520$	$270$	$1.01898$	$3.42152$	$[0, 0, 0, 5, -10]$	\(y^2=x^3+5x-10\)	8.2.0.a.1	$[]$