Elliptic curves over $\Q$ of conductor 384

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
384.a1	384g1	384.a	384g	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{8} \cdot 3^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.360101$	$19056256/27$	$1.04486$	$3.74885$	$[0, -1, 0, -35, -69]$	\(y^2=x^3-x^2-35x-69\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.a2	384g2	384.a	384g	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{13} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$96$	$-0.013528$	$-219488/729$	$1.06277$	$3.90175$	$[0, -1, 0, -25, -119]$	\(y^2=x^3-x^2-25x-119\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$
384.b1	384d1	384.b	384d	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{8} \cdot 3 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$0.639465641$	$1$		$5$	$16$	$-0.728445$	$16000/3$	$0.92547$	$2.55863$	$[0, -1, 0, -3, 3]$	\(y^2=x^3-x^2-3x+3\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[(2, 1)]$
384.b2	384d2	384.b	384d	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{13} \cdot 3^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$0.319732820$	$1$		$11$	$32$	$-0.381871$	$4000/9$	$0.97488$	$3.08631$	$[0, -1, 0, 7, 9]$	\(y^2=x^3-x^2+7x+9\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[(1, 4)]$
384.c1	384b2	384.c	384b	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{14} \cdot 3 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$32$	$-0.381871$	$16000/3$	$0.92547$	$3.25753$	$[0, -1, 0, -13, -11]$	\(y^2=x^3-x^2-13x-11\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.c2	384b1	384.c	384b	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{7} \cdot 3^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$16$	$-0.728445$	$4000/9$	$0.97488$	$2.38741$	$[0, -1, 0, 2, -2]$	\(y^2=x^3-x^2+2x-2\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$
384.d1	384f2	384.d	384f	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{14} \cdot 3^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$96$	$-0.013528$	$19056256/27$	$1.04486$	$4.44775$	$[0, -1, 0, -141, 693]$	\(y^2=x^3-x^2-141x+693\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.d2	384f1	384.d	384f	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{7} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.360101$	$-219488/729$	$1.06277$	$3.20285$	$[0, -1, 0, -6, 18]$	\(y^2=x^3-x^2-6x+18\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$
384.e1	384h1	384.e	384h	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{8} \cdot 3^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$0.271689568$	$1$		$9$	$48$	$-0.360101$	$19056256/27$	$1.04486$	$3.74885$	$[0, 1, 0, -35, 69]$	\(y^2=x^3+x^2-35x+69\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[(1, 6)]$
384.e2	384h2	384.e	384h	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{13} \cdot 3^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$0.135844784$	$1$		$17$	$96$	$-0.013528$	$-219488/729$	$1.06277$	$3.90175$	$[0, 1, 0, -25, 119]$	\(y^2=x^3+x^2-25x+119\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[(-1, 12)]$
384.f1	384c2	384.f	384c	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{14} \cdot 3 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$32$	$-0.381871$	$16000/3$	$0.92547$	$3.25753$	$[0, 1, 0, -13, 11]$	\(y^2=x^3+x^2-13x+11\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.f2	384c1	384.f	384c	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{7} \cdot 3^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$16$	$-0.728445$	$4000/9$	$0.97488$	$2.38741$	$[0, 1, 0, 2, 2]$	\(y^2=x^3+x^2+2x+2\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$
384.g1	384a1	384.g	384a	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{8} \cdot 3 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$16$	$-0.728445$	$16000/3$	$0.92547$	$2.55863$	$[0, 1, 0, -3, -3]$	\(y^2=x^3+x^2-3x-3\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.g2	384a2	384.g	384a	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{13} \cdot 3^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$32$	$-0.381871$	$4000/9$	$0.97488$	$3.08631$	$[0, 1, 0, 7, -9]$	\(y^2=x^3+x^2+7x-9\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$
384.h1	384e2	384.h	384e	$2$	$2$	\( 2^{7} \cdot 3 \)	\( 2^{14} \cdot 3^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$24$	$12$	$0$	$1$	$1$		$1$	$96$	$-0.013528$	$19056256/27$	$1.04486$	$4.44775$	$[0, 1, 0, -141, -693]$	\(y^2=x^3+x^2-141x-693\)	2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1	$[]$
384.h2	384e1	384.h	384e	$2$	$2$	\( 2^{7} \cdot 3 \)	\( - 2^{7} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$24$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.360101$	$-219488/729$	$1.06277$	$3.20285$	$[0, 1, 0, -6, -18]$	\(y^2=x^3+x^2-6x-18\)	2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1	$[]$