Elliptic curves over $\Q$ of conductor 8048

Results (12 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
8048.a1	8048i1	8048.a	8048i	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{12} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.476329999$	$1$		$16$	$2432$	$-0.100365$	$658503/503$	$0.73029$	$2.41466$	$[0, 0, 0, 29, 34]$	\(y^2=x^3+29x+34\)	1006.2.0.?	$[(1, 8), (-1, 2)]$
8048.b1	8048f1	8048.b	8048f	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{16} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.822811011$	$1$		$12$	$2304$	$0.131950$	$13651919/8048$	$0.83435$	$2.75177$	$[0, -1, 0, 80, -64]$	\(y^2=x^3-x^2+80x-64\)	1006.2.0.?	$[(8, 32), (2, 10)]$
8048.c1	8048g1	8048.c	8048g	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{12} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.492301529$	$1$		$14$	$6400$	$0.546307$	$-1024497361441/503$	$0.93909$	$4.00003$	$[0, -1, 0, -3360, 76096]$	\(y^2=x^3-x^2-3360x+76096\)	1006.2.0.?	$[(34, 2), (40, 64)]$
8048.d1	8048j1	8048.d	8048j	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{16} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.712606191$	$1$		$6$	$1152$	$0.123471$	$-389017/8048$	$0.80210$	$2.75690$	$[0, -1, 0, -24, -272]$	\(y^2=x^3-x^2-24x-272\)	1006.2.0.?	$[(12, 32)]$
8048.e1	8048k1	8048.e	8048k	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{12} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.320541258$	$1$		$6$	$1408$	$0.226416$	$-3463512697/503$	$0.83466$	$3.36739$	$[0, -1, 0, -504, 4528]$	\(y^2=x^3-x^2-504x+4528\)	1006.2.0.?	$[(12, 8)]$
8048.f1	8048d2	8048.f	8048d	$2$	$2$	\( 2^{4} \cdot 503 \)	\( 2^{15} \cdot 503^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$3024$	$0.593870$	$3687953625/2024072$	$0.91410$	$3.37435$	$[0, 0, 0, -515, -1022]$	\(y^2=x^3-515x-1022\)	2.3.0.a.1, 8.6.0.b.1, 2012.6.0.?, 4024.12.0.?	$[]$
8048.f2	8048d1	8048.f	8048d	$2$	$2$	\( 2^{4} \cdot 503 \)	\( - 2^{18} \cdot 503 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$1512$	$0.247296$	$52734375/32192$	$1.25681$	$2.90204$	$[0, 0, 0, 125, -126]$	\(y^2=x^3+125x-126\)	2.3.0.a.1, 8.6.0.c.1, 1006.6.0.?, 4024.12.0.?	$[]$
8048.g1	8048e1	8048.g	8048e	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$2880$	$0.498752$	$-1349232625/515072$	$0.83497$	$3.31887$	$[0, 1, 0, -368, -3628]$	\(y^2=x^3+x^2-368x-3628\)	1006.2.0.?	$[]$
8048.h1	8048a1	8048.h	8048a	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{10} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.424095725$	$1$		$4$	$832$	$-0.069140$	$-74438500/503$	$0.76253$	$2.78751$	$[0, 1, 0, -88, 292]$	\(y^2=x^3+x^2-88x+292\)	1006.2.0.?	$[(6, 4)]$
8048.i1	8048c1	8048.i	8048c	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{8} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$768$	$-0.331223$	$686000/503$	$0.67133$	$2.11091$	$[0, 1, 0, 12, -4]$	\(y^2=x^3+x^2+12x-4\)	1006.2.0.?	$[]$
8048.j1	8048b1	8048.j	8048b	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{10} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.466933085$	$1$		$4$	$640$	$-0.172230$	$-3650692/503$	$0.71271$	$2.47471$	$[0, 1, 0, -32, 68]$	\(y^2=x^3+x^2-32x+68\)	1006.2.0.?	$[(2, 4)]$
8048.k1	8048h1	8048.k	8048h	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{24} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$4$	$2$	$0$	$11520$	$0.734588$	$-270212594625/2060288$	$0.90140$	$3.85329$	$[0, 0, 0, -2155, -38758]$	\(y^2=x^3-2155x-38758\)	1006.2.0.?	$[]$