Elliptic curves over $\Q$ of conductor 675

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
675.a1	675h1	675.a	675h	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{11} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$864$	$0.769298$	$-12288/25$	$0.90890$	$5.01408$	$[0, 0, 1, -675, -14344]$	\(y^2+y=x^3-675x-14344\)	6.2.0.a.1	$[]$
675.b1	675b1	675.b	675b	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( 3^{5} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$60$	$40$	$1$	$0.131955364$	$1$		$8$	$36$	$-0.582679$	$1875$	$1.20397$	$2.49409$	$[1, -1, 1, -5, 2]$	\(y^2+xy+y=x^3-x^2-5x+2\)	5.10.0.a.1, 12.2.0.a.1, 15.20.0.b.1, 20.20.0.c.1, 60.40.1.n.1	$[(0, 1)]$
675.c1	675d1	675.c	675d	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( 3^{11} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$60$	$40$	$1$	$1$	$1$		$0$	$540$	$0.771347$	$1875$	$1.20397$	$4.98819$	$[1, -1, 1, -1055, -3428]$	\(y^2+xy+y=x^3-x^2-1055x-3428\)	5.10.0.a.1, 12.2.0.a.1, 15.20.0.b.1, 20.20.0.c.1, 60.40.1.n.1	$[]$
675.d1	675c2	675.d	675c	$2$	$3$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{9} \cdot 5^{4} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.4	3B.1.2				$1$	$1$		$0$	$126$	$0.039321$	$0$		$3.65020$	$[0, 0, 1, 0, -169]$	\(y^2+y=x^3-169\)		$[]$
675.d2	675c1	675.d	675c	$2$	$3$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{4} \)	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.1	3B.1.1				$1$	$1$		$2$	$42$	$-0.509985$	$0$		$2.63838$	$[0, 0, 1, 0, 6]$	\(y^2+y=x^3+6\)		$[]$
675.e1	675a4	675.e	675a	$4$	$27$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{11} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓							$3.650319782$	$1$		$2$	$432$	$0.856867$	$-12288000$	$1.23864$	$5.84303$	$[0, 0, 1, -6750, -213469]$	\(y^2+y=x^3-6750x-213469\)		$[(145, 1362)]$
675.e2	675a3	675.e	675a	$4$	$27$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{5} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓							$0.135197028$	$1$		$8$	$144$	$0.307561$	$-12288000$	$1.23864$	$4.83121$	$[0, 0, 1, -750, 7906]$	\(y^2+y=x^3-750x+7906\)		$[(10, 37)]$
675.e3	675a2	675.e	675a	$4$	$27$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{9} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.972.55.16	3Cs				$1.216773260$	$1$		$4$	$144$	$0.307561$	$0$		$4.14429$	$[0, 0, 1, 0, -844]$	\(y^2+y=x^3-844\)		$[(10, 12)]$
675.e4	675a1	675.e	675a	$4$	$27$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.972.55.16	3Cs				$0.405591086$	$1$		$4$	$48$	$-0.241745$	$0$		$3.13248$	$[0, 0, 1, 0, 31]$	\(y^2+y=x^3+31\)		$[(5, 12)]$
675.f1	675e2	675.f	675e	$2$	$3$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{9} \cdot 5^{10} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$630$	$0.844040$	$0$		$5.13248$	$[0, 0, 1, 0, -21094]$	\(y^2+y=x^3-21094\)		$[]$
675.f2	675e1	675.f	675e	$2$	$3$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{10} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$0$	$210$	$0.294734$	$0$		$4.12066$	$[0, 0, 1, 0, 781]$	\(y^2+y=x^3+781\)		$[]$
675.g1	675i1	675.g	675i	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( 3^{5} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$60$	$40$	$1$	$0.508507719$	$1$		$2$	$180$	$0.222041$	$1875$	$1.20397$	$3.97637$	$[1, -1, 0, -117, 166]$	\(y^2+xy=x^3-x^2-117x+166\)	5.10.0.a.1, 12.2.0.a.1, 15.20.0.b.1, 20.20.0.c.1, 60.40.1.n.1	$[(-6, 28)]$
675.h1	675f1	675.h	675f	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( 3^{11} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$60$	$40$	$1$	$1$	$1$		$0$	$108$	$-0.033372$	$1875$	$1.20397$	$3.50591$	$[1, -1, 0, -42, -19]$	\(y^2+xy=x^3-x^2-42x-19\)	5.10.0.a.1, 12.2.0.a.1, 15.20.0.b.1, 20.20.0.c.1, 60.40.1.n.1	$[]$
675.i1	675g1	675.i	675g	$1$	$1$	\( 3^{3} \cdot 5^{2} \)	\( - 3^{5} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$288$	$0.219991$	$-12288/25$	$0.90890$	$4.00227$	$[0, 0, 1, -75, 531]$	\(y^2+y=x^3-75x+531\)	6.2.0.a.1	$[]$