Elliptic curves over $\Q$ of conductor 1003

Results (4 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
1003.a1	1003c1	1003.a	1003c	$1$	$1$	\( 17 \cdot 59 \)	\( - 17^{2} \cdot 59^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$1$	$1$		$0$	$384$	$0.175883$	$28066748319/59354531$	$0.88784$	$3.62248$	$[1, -1, 1, 63, -332]$	\(y^2+xy+y=x^3-x^2+63x-332\)	118.2.0.?	$[]$
1003.b1	1003a1	1003.b	1003a	$1$	$1$	\( 17 \cdot 59 \)	\( - 17 \cdot 59 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2006$	$2$	$0$	$0.701450453$	$1$		$2$	$36$	$-0.744081$	$32768/1003$	$0.73981$	$2.07595$	$[0, -1, 1, 1, 1]$	\(y^2+y=x^3-x^2+x+1\)	2006.2.0.?	$[(1, 1)]$
1003.c1	1003b1	1003.c	1003b	$1$	$1$	\( 17 \cdot 59 \)	\( - 17^{2} \cdot 59 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$118$	$2$	$0$	$1$	$1$		$0$	$48$	$-0.477463$	$-47045881/17051$	$0.87596$	$2.62677$	$[1, 0, 1, -8, -11]$	\(y^2+xy+y=x^3-8x-11\)	118.2.0.?	$[]$
1003.d1	1003d1	1003.d	1003d	$1$	$1$	\( 17 \cdot 59 \)	\( - 17 \cdot 59^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2006$	$2$	$0$	$0.545993865$	$1$		$0$	$180$	$-0.038056$	$-7622111232/3491443$	$0.84891$	$3.37697$	$[0, 0, 1, -41, 135]$	\(y^2+y=x^3-41x+135\)	2006.2.0.?	$[(9/2, 55/2)]$