Elliptic curves over $\Q$ of conductor 3864

Results (11 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
3864.a1	3864b1	3864.a	3864b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{11} \cdot 3^{5} \cdot 7^{3} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$2400$	$0.543468$	$-3261064466/1917027$	$[0, -1, 0, -392, -4116]$	\(y^2=x^3-x^2-392x-4116\)
3864.b1	3864a2	3864.b	3864a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$1$	$1$		$1$	$10752$	$1.300497$	$1566789944863250/925924041$	$[0, -1, 0, -30728, -2061972]$	\(y^2=x^3-x^2-30728x-2061972\)
3864.b2	3864a1	3864.b	3864a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{12} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1$	$1$		$1$	$5376$	$0.953924$	$-416618810500/598934007$	$[0, -1, 0, -1568, -44100]$	\(y^2=x^3-x^2-1568x-44100\)
3864.c1	3864c1	3864.c	3864c	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{7} \cdot 7 \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.097771173$	$1$		$10$	$1120$	$0.205352$	$128000/352107$	$[0, 1, 0, 7, 459]$	\(y^2=x^3+x^2+7x+459\)
3864.d1	3864e3	3864.d	3864e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.58	2B	$1$	$4$	$2$	$1$	$8192$	$1.160669$	$369937818893666/123409881$	$[0, 1, 0, -18992, -1013472]$	\(y^2=x^3+x^2-18992x-1013472\)
3864.d2	3864e4	3864.d	3864e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.103	2B	$1$	$1$		$1$	$8192$	$1.160669$	$48260105780546/1193313807$	$[0, 1, 0, -9632, 352800]$	\(y^2=x^3+x^2-9632x+352800\)
3864.d3	3864e2	3864.d	3864e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.1	2Cs	$1$	$1$		$3$	$4096$	$0.814096$	$267100692772/102880449$	$[0, 1, 0, -1352, -11520]$	\(y^2=x^3+x^2-1352x-11520\)
3864.d4	3864e1	3864.d	3864e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.50	2B	$1$	$1$		$3$	$2048$	$0.467523$	$8284506032/7394247$	$[0, 1, 0, 268, -1152]$	\(y^2=x^3+x^2+268x-1152\)
3864.e1	3864d2	3864.e	3864d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2560$	$0.660947$	$26860713266/7394247$	$[0, 1, 0, -792, -6480]$	\(y^2=x^3+x^2-792x-6480\)
3864.e2	3864d1	3864.e	3864d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{4} \cdot 7 \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1280$	$0.314373$	$224727548/299943$	$[0, 1, 0, 128, -592]$	\(y^2=x^3+x^2+128x-592\)
3864.f1	3864f1	3864.f	3864f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3 \cdot 7^{3} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$1632$	$0.136544$	$-3525581824/23667$	$[0, 1, 0, -201, -1173]$	\(y^2=x^3+x^2-201x-1173\)