Elliptic curves over $\Q$ of conductor 6896

Results (14 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
6896.a1	6896f1	6896.a	6896f	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{12} \cdot 431 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$0.280170473$	$1$		$20$	$2560$	$0.038820$	$-72511713/431$	$0.79853$	$2.98995$	$[0, 0, 0, -139, 634]$	\(y^2=x^3-139x+634\)	862.2.0.?	$[(5, 8), (7, 2)]$
6896.b1	6896j2	6896.b	6896j	$2$	$3$	\( 2^{4} \cdot 431 \)	\( - 2^{16} \cdot 431^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$5172$	$16$	$0$	$0.279705716$	$1$		$6$	$10368$	$1.121115$	$-41314084993/1281007856$	$0.94098$	$4.15920$	$[0, -1, 0, -1152, 111616]$	\(y^2=x^3-x^2-1152x+111616\)	3.4.0.a.1, 12.8.0-3.a.1.2, 862.2.0.?, 2586.8.0.?, 5172.16.0.?	$[(576, 13792)]$
6896.b2	6896j1	6896.b	6896j	$2$	$3$	\( 2^{4} \cdot 431 \)	\( - 2^{24} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$5172$	$16$	$0$	$0.839117148$	$1$		$4$	$3456$	$0.571809$	$56181887/1765376$	$0.88358$	$3.40975$	$[0, -1, 0, 128, -4096]$	\(y^2=x^3-x^2+128x-4096\)	3.4.0.a.1, 12.8.0-3.a.1.1, 862.2.0.?, 2586.8.0.?, 5172.16.0.?	$[(64, 512)]$
6896.c1	6896i1	6896.c	6896i	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{14} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$0.508388665$	$1$		$4$	$768$	$-0.003513$	$357911/1724$	$0.76407$	$2.61316$	$[0, -1, 0, 24, 112]$	\(y^2=x^3-x^2+24x+112\)	862.2.0.?	$[(4, 16)]$
6896.d1	6896a1	6896.d	6896a	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{8} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$1.641171123$	$1$		$2$	$448$	$-0.296745$	$-3631696/431$	$0.68680$	$2.35747$	$[0, -1, 0, -20, -32]$	\(y^2=x^3-x^2-20x-32\)	862.2.0.?	$[(8, 16)]$
6896.e1	6896h1	6896.e	6896h	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{12} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$0.463019734$	$1$		$6$	$640$	$-0.122459$	$-1/431$	$0.92493$	$2.47079$	$[0, -1, 0, 0, 64]$	\(y^2=x^3-x^2+64\)	862.2.0.?	$[(0, 8)]$
6896.f1	6896b1	6896.f	6896b	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{10} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$0.511293482$	$1$		$4$	$640$	$-0.230095$	$415292/431$	$0.69869$	$2.24787$	$[0, -1, 0, 16, 16]$	\(y^2=x^3-x^2+16x+16\)	862.2.0.?	$[(0, 4)]$
6896.g1	6896g2	6896.g	6896g	$2$	$2$	\( 2^{4} \cdot 431 \)	\( 2^{15} \cdot 431^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$3448$	$12$	$0$	$1.637698412$	$1$		$3$	$2592$	$0.578764$	$4227952113/1486088$	$1.02426$	$3.44878$	$[0, 0, 0, -539, 3018]$	\(y^2=x^3-539x+3018\)	2.3.0.a.1, 8.6.0.b.1, 1724.6.0.?, 3448.12.0.?	$[(-19, 80)]$
6896.g2	6896g1	6896.g	6896g	$2$	$2$	\( 2^{4} \cdot 431 \)	\( - 2^{18} \cdot 431 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$3448$	$12$	$0$	$3.275396825$	$1$		$3$	$1296$	$0.232190$	$27818127/27584$	$0.87279$	$2.88040$	$[0, 0, 0, 101, 330]$	\(y^2=x^3+101x+330\)	2.3.0.a.1, 8.6.0.c.1, 862.6.0.?, 3448.12.0.?	$[(47, 330)]$
6896.h1	6896e1	6896.h	6896e	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{20} \cdot 431 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$1.682895742$	$1$		$10$	$3072$	$0.340219$	$-912673/110336$	$0.86812$	$3.09871$	$[0, 1, 0, -32, -1036]$	\(y^2=x^3+x^2-32x-1036\)	862.2.0.?	$[(26, 128), (106/3, 512/3)]$
6896.i1	6896c1	6896.i	6896c	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{8} \cdot 431 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$1$	$1$		$0$	$704$	$-0.198758$	$-61918288/431$	$0.74036$	$2.65859$	$[0, 1, 0, -52, -164]$	\(y^2=x^3+x^2-52x-164\)	862.2.0.?	$[]$
6896.j1	6896d1	6896.j	6896d	$2$	$5$	\( 2^{4} \cdot 431 \)	\( - 2^{32} \cdot 431 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$8620$	$48$	$1$	$1$	$4$	$2$	$0$	$15360$	$1.336376$	$-1646417855125441/451936256$	$0.94554$	$4.90520$	$[0, 1, 0, -39360, -3019468]$	\(y^2=x^3+x^2-39360x-3019468\)	5.12.0.a.1, 20.24.0-5.a.1.2, 862.2.0.?, 4310.24.1.?, 8620.48.1.?	$[]$
6896.j2	6896d2	6896.j	6896d	$2$	$5$	\( 2^{4} \cdot 431 \)	\( - 2^{16} \cdot 431^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$8620$	$48$	$1$	$1$	$4$	$2$	$0$	$76800$	$2.141094$	$402337908227545919/237961300338416$	$1.02084$	$5.52727$	$[0, 1, 0, 246080, 7054132]$	\(y^2=x^3+x^2+246080x+7054132\)	5.12.0.a.2, 20.24.0-5.a.2.2, 862.2.0.?, 4310.24.1.?, 8620.48.1.?	$[]$
6896.k1	6896k1	6896.k	6896k	$1$	$1$	\( 2^{4} \cdot 431 \)	\( - 2^{18} \cdot 431 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$862$	$2$	$0$	$3.942434012$	$1$		$0$	$4608$	$0.480247$	$-38238692409/27584$	$0.88652$	$3.69807$	$[0, 0, 0, -1123, -14494]$	\(y^2=x^3-1123x-14494\)	862.2.0.?	$[(409/3, 4544/3)]$