Elliptic curves over Q\Q of conductor 540

Results (12 matches)

  Download displayed columns for results to

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
540.a1	540d2	540.a	540d	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{11} \cdot 5^{3}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$3.716854919$	$1$		$2$	$324$	$0.426794$	$-5267712/125$	$1.15142$	$4.82783$	$[0, 0, 0, -513, -4563]$	$y^2=x^3-513x-4563$	3.8.0-3.a.1.1, 30.16.0-30.b.1.2	$[(28, 55)]$
540.a2	540d1	540.a	540d	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{9} \cdot 5$	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1.238951639$	$1$		$10$	$108$	$-0.122512$	$6912/5$	$0.69897$	$3.41745$	$[0, 0, 0, 27, -27]$	$y^2=x^3+27x-27$	3.8.0-3.a.1.2, 30.16.0-30.b.1.4	$[(1, 1)]$
540.b1	540c1	540.b	540c	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{8} \cdot 3^{9} \cdot 5^{2}$	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$0.505482570$	$1$		$12$	$216$	$0.409268$	$-5971968/25$	$1.09044$	$4.93398$	$[0, 0, 0, -648, 6372]$	$y^2=x^3-648x+6372$	3.8.0-3.a.1.2, 6.16.0-6.b.1.2	$[(21, 45)]$
540.b2	540c2	540.b	540c	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{8} \cdot 3^{11} \cdot 5^{6}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$1.516447711$	$1$		$2$	$648$	$0.958574$	$8429568/15625$	$1.06918$	$5.46239$	$[0, 0, 0, 1512, 33588]$	$y^2=x^3+1512x+33588$	3.8.0-3.a.1.1, 6.16.0-6.b.1.1	$[(-11, 125)]$
540.c1	540a1	540.c	540a	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{3} \cdot 5$	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1$	$1$		$2$	$36$	$-0.411483$	$-9199872/5$	$0.95440$	$3.51328$	$[0, 0, 0, -33, 73]$	$y^2=x^3-33x+73$	3.8.0-3.a.1.2, 30.16.0-30.b.1.4	$[]$
540.c2	540a2	540.c	540a	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{9} \cdot 5^{3}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$1$	$1$		$0$	$108$	$0.137823$	$6912/125$	$1.02720$	$3.95936$	$[0, 0, 0, 27, 297]$	$y^2=x^3+27x+297$	3.8.0-3.a.1.1, 30.16.0-30.b.1.2	$[]$
540.d1	540b2	540.d	540b	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{5} \cdot 5^{3}$	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$0.218874210$	$1$		$18$	$108$	$-0.122512$	$-5267712/125$	$1.15142$	$3.78013$	$[0, 0, 0, -57, 169]$	$y^2=x^3-57x+169$	3.8.0-3.a.1.2, 30.16.0-30.b.1.4	$[(5, 3)]$
540.d2	540b1	540.d	540b	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{3} \cdot 5$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$0.656622630$	$1$		$2$	$36$	$-0.671818$	$6912/5$	$0.69897$	$2.36975$	$[0, 0, 0, 3, 1]$	$y^2=x^3+3x+1$	3.8.0-3.a.1.1, 30.16.0-30.b.1.2	$[(0, 1)]$
540.e1	540e1	540.e	540e	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{8} \cdot 3^{3} \cdot 5^{2}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$1$	$1$		$0$	$72$	$-0.140038$	$-5971968/25$	$1.09044$	$3.88628$	$[0, 0, 0, -72, -236]$	$y^2=x^3-72x-236$	3.8.0-3.a.1.1, 6.16.0-6.b.1.1	$[]$
540.e2	540e2	540.e	540e	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{8} \cdot 3^{5} \cdot 5^{6}$	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$1$	$1$		$2$	$216$	$0.409268$	$8429568/15625$	$1.06918$	$4.41469$	$[0, 0, 0, 168, -1244]$	$y^2=x^3+168x-1244$	3.8.0-3.a.1.2, 6.16.0-6.b.1.2	$[]$
540.f1	540f2	540.f	540f	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{9} \cdot 5$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$1$	$1$		$0$	$108$	$0.137823$	$-9199872/5$	$0.95440$	$4.56098$	$[0, 0, 0, -297, -1971]$	$y^2=x^3-297x-1971$	3.8.0-3.a.1.1, 30.16.0-30.b.1.2	$[]$
540.f2	540f1	540.f	540f	$2$	$3$	$2^{2} \cdot 3^{3} \cdot 5$	$- 2^{4} \cdot 3^{3} \cdot 5^{3}$	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1$	$1$		$2$	$36$	$-0.411483$	$6912/125$	$1.02720$	$2.91166$	$[0, 0, 0, 3, -11]$	$y^2=x^3+3x-11$	3.8.0-3.a.1.2, 30.16.0-30.b.1.4	$[]$

  Download displayed columns for results to