Elliptic curves over $\Q$ of conductor 270

Results (8 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
270.a1	270a1	270.a	270a	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2 \cdot 3^{9} \cdot 5 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$		$2$	$36$	$-0.279375$	$-19683/10$	$1.02991$	$3.64481$	$[1, -1, 0, -15, 35]$	\(y^2+xy=x^3-x^2-15x+35\)	3.8.0-3.a.1.2, 120.16.0.?	$[]$
270.a2	270a2	270.a	270a	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$		$0$	$108$	$0.269931$	$1073733/1000$	$0.96044$	$4.63905$	$[1, -1, 0, 120, -424]$	\(y^2+xy=x^3-x^2+120x-424\)	3.8.0-3.a.1.1, 120.16.0.?	$[]$
270.b1	270d1	270.b	270d	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{5} \cdot 3^{3} \cdot 5^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$		$2$	$60$	$-0.045373$	$-16522921323/4000$	$1.05582$	$4.79140$	$[1, -1, 0, -159, 813]$	\(y^2+xy=x^3-x^2-159x+813\)	3.8.0-3.a.1.2, 120.16.0.?	$[]$
270.b2	270d2	270.b	270d	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{15} \cdot 3^{9} \cdot 5 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$		$0$	$180$	$0.503934$	$1601613/163840$	$1.15089$	$5.24133$	$[1, -1, 0, 66, 2708]$	\(y^2+xy=x^3-x^2+66x+2708\)	3.8.0-3.a.1.1, 120.16.0.?	$[]$
270.c1	270b2	270.c	270b	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{5} \cdot 3^{9} \cdot 5^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$		$0$	$180$	$0.503934$	$-16522921323/4000$	$1.05582$	$5.96881$	$[1, -1, 1, -1433, -20519]$	\(y^2+xy+y=x^3-x^2-1433x-20519\)	3.8.0-3.a.1.1, 120.16.0.?	$[]$
270.c2	270b1	270.c	270b	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{15} \cdot 3^{3} \cdot 5 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$		$2$	$60$	$-0.045373$	$1601613/163840$	$1.15089$	$4.06392$	$[1, -1, 1, 7, -103]$	\(y^2+xy+y=x^3-x^2+7x-103\)	3.8.0-3.a.1.2, 120.16.0.?	$[]$
270.d1	270c1	270.d	270c	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2 \cdot 3^{3} \cdot 5 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$		$0$	$12$	$-0.828681$	$-19683/10$	$1.02991$	$2.46739$	$[1, -1, 1, -2, -1]$	\(y^2+xy+y=x^3-x^2-2x-1\)	3.8.0-3.a.1.1, 120.16.0.?	$[]$
270.d2	270c2	270.d	270c	$2$	$3$	\( 2 \cdot 3^{3} \cdot 5 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$		$2$	$36$	$-0.279375$	$1073733/1000$	$0.96044$	$3.46164$	$[1, -1, 1, 13, 11]$	\(y^2+xy+y=x^3-x^2+13x+11\)	3.8.0-3.a.1.2, 120.16.0.?	$[]$